(a) The total Coulomb force (in N) on a charge is F = 0.090 NThe direction of the force is repulsive as the two charges are both positive.(b) The x-position where the electric field is zero is 8.22 cm.
(a) The formula for Coulomb's law is:F = (1/4πε) * (q1 * q2 / r²)where ε = permittivity of free space = 8.85 × 10−12 N−1 m−2 C²F = force in Nq1 = 9.00 nCq2 = 6.50 μC = 6.50 × 10−6CThe distance between the charges can be found from the diagram to be:r = 8.0 cm + 4.5 cm = 12.5 cm = 0.125 m.
Therefore, plugging in the values in Coulomb's law equation:F = (1/4πε) * (q1 * q2 / r²)F = (1/4π(8.85 × 10−12 N−1 m−2 C²)) * (9.00 × 10−9C) * (6.50 × 10−6C) / (0.125m)²F = 0.090 NThe direction of the force is repulsive as the two charges are both positive.
(b) To find the x-position at which the electric field is zero, we can use the concept of electric potential.The electric potential at any point due to a point charge is given by:V = (1/4πε) * (q / r)where r = distance between the charge and the point where potential is to be found.
For charges distributed along an axis (as in this case), we can add up the potentials due to all the charges.To find the point where the electric field is zero, we can imagine a positive test charge being placed at different positions along the axis and find at which point the test charge does not experience any force.
The potential at a point on the x-axis at distance x from the first charge q1 is:V1 = (1/4πε) * (q1 / x)V2 = (1/4πε) * (q2 / (14cm - x))At the point where the electric field is zero, V1 + V2 = 0Substituting the given values:V1 + V2 = (1/4π(8.85 × 10−12 N−1 m−2 C²)) * (9.00 × 10−9C) / x + (1/4π(8.85 × 10−12 N−1 m−2 C²)) * (6.50 × 10−6C) / (14cm - x)= 0.
Solving this equation gives the value of x as 8.22 cm (rounded off to two decimal places).Therefore, the x-position where the electric field is zero is 8.22 cm.
Part (a)The force between two point charges is given by Coulomb's Law. The formula for Coulomb's law is:F = (1/4πε) * (q1 * q2 / r²)where F = force in Nε = permittivity of free space = 8.85 × 10−12 N−1 m−2 C²q1 = 9.00 nCq2 = 6.50 μC = 6.50 × 10−6Cr = 8.0 cm + 4.5 cm = 12.5 cm = 0.125 mTherefore, plugging in the values in Coulomb's law equation:F = (1/4π(8.85 × 10−12 N−1 m−2 C²)) * (9.00 × 10−9C) * (6.50 × 10−6C) / (0.125m)²F = 0.090 NThe direction of the force is repulsive as the two charges are both positive.
Part (b)The potential at a point on the x-axis at distance x from the first charge q1 is:V1 = (1/4πε) * (q1 / x)V2 = (1/4πε) * (q2 / (14cm - x))At the point where the electric field is zero, V1 + V2 = 0Substituting the given values:V1 + V2 = (1/4π(8.85 × 10−12 N−1 m−2 C²)) * (9.00 × 10−9C) / x + (1/4π(8.85 × 10−12 N−1 m−2 C²)) * (6.50 × 10−6C) / (14cm - x)= 0.
Solving this equation gives the value of x as 8.22 cm (rounded off to two decimal places).Therefore, the x-position where the electric field is zero is 8.22 cm.
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A 14 V battery delivers 104 mA of current when connected to a 74 Ω resistor. Determine the internal resistance of the battery. Answer in units of Ω.
The internal resistance of the battery is 60.5 Ω (approx).
Voltage of battery (V) = 14 V
Current passing through it (I) = 104 mA = 0.104 A
Resistance of the resistor (R) = 74 Ω
To find the internal resistance of the battery, use the formula;
Voltage of battery (V) = Current passing through it (I) × (Resistance of the resistor (R) + Internal resistance of the battery (r))
Putting the above values in the formula we get:
14 V = 0.104 A × (74 Ω + r)
14 V = 7.696 Ω + 0.104 r
0.104 r = 14 V - 7.696 Ω
0.104 r = 6.304 Ω
r = 6.304 / 0.104 Ω
r = 60.5 Ω (approx)
Therefore, the internal resistance of the battery is 60.5 Ω (approx).
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A billiard cue ball with a mass of 0.60 kg and an eight ball with a mass of 0.55 kg are rolled toward each other. The cue ball has a velocity of 3.0 m/s heading east and the eight ball has a velocity of 2.0 m/s heading north. After the collision, the cue ball moves off at a velocity of 2.0 m/s 40⁰ north of east.
What is net momentum of the system above before and after the collision?
What north component (y-component) of the momentum of the cue ball after collision?
Using your responses above, determine the final velocity of the eight ball:
The net momentum of the system before the collision is given by the expression: Momentum before = m1v1 + m2v2where m1 and v1 are the mass and velocity of the cue ball respectively and m2 and v2 are the mass and velocity of the eight ball respectively.
Substituting in the given values, we have:Momentum before = (0.6 kg) (3.0 m/s) + (0.55 kg) (2.0 m/s) = 1.80 kg m/s + 1.10 kg m/s = 2.90 kg m/s. The net momentum of the system after the collision is given by the expression:Momentum after = m1v1' + m2v2'where v1' and v2' are the velocities of the cue ball and eight ball respectively after the collision.
Substituting in the given values, we have: Momentum after = (0.6 kg) (2.0 m/s cos 40°) + (0.55 kg) (v2')Momentum after = 1.20 cos 40° kg m/s + (0.55 kg) (v2')Momentum after = 0.92 kg m/s + 0.55 kg v2'Conservation of momentum principle states that the total momentum before the collision must equal the total momentum after the collision: Momentum before = Momentum after2.90 kg m/s = 0.92 kg m/s + 0.55 kg v2'Solving for v2', we get:v2' = (2.90 kg m/s - 0.92 kg m/s) / 0.55 kgv2' = 4.71 m/s.
The north component (y-component) of the momentum of the cue ball after collision is given by the expression:py = m1v1' sin θSubstituting the given values, we have:py = (0.6 kg) (2.0 m/s sin 40°)py = 0.78 kg m/sTherefore, the final velocity of the eight ball is 4.71 m/s.
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A cord is used to vertically lower an initially stationary block of mass M-12 kg at a constant downward acceleration of g/5. When the block has fallen a distance d = 3.9 m, find (a) the work done by the cord's force on the block. (b) the work done by the gravitational force on the block, (c) the kinetic energy of the block, and (d) the speed of the block. (Note: Take the downward direction positive) (a) Number ______________ Units ________________
(b) Number ______________ Units ________________
(c) Number ______________ Units ________________
(d) Number ______________ Units ________________
A cord is used to vertically lower an initially stationary block of mass M-12 kg at a constant downward acceleration of g/5
Mass of the block, M = 12 kg
When the block has fallen a distance d = 3.9 m, acceleration of the block, a = g/5 = 9.8/5 m/s² = 1.96 m/s²
We know that work done is given by W = Fs
Here, downward acceleration, a = 1.96 m/s²
Gravitational force acting on the block = Mg = 12 × 9.8 = 117.6 N (taking downward direction positive)
(a) The work done by the cord's force on the block
F = Ma = 12 × 1.96 = 23.52 NW = Fs = 23.52 × 3.9 = 91.728 J
(b) The work done by the gravitational force on the block
W = F × d = 117.6 × 3.9 = 459.84 J
(c) The kinetic energy of the block
When the block falls a distance d, the potential energy is converted into kinetic energy.
In other words, Potential Energy + Work done = Kinetic Energy (mv²)/2mgd + Fd = (mv²)/2v² = 2gd + (2Fd)/mv² = 2 × 9.8 × 3.9 + (2 × 117.6 × 3.9)/12v² = 76.44v = √76.44m/s
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Which pairs of angles must atways be the same? Select one: a. Angle of incidence and angle of reflection b. Angle of incidence and angle of refraction c. Angle of reflection and angle of refraction d. Angle of incidence and angle of diffraction Two waves cross and result in a wave with a targer amplitude than either of the originat waves, This is called Select one: a. phase exchange b. negative superimposition c. destructive interference d. constructive interference
The angles that must always be the same are the angle of incidence and the angle of reflection (a). When two waves cross and result in a wave with a larger amplitude than either of the original waves, it is called constructive interference (d).
(a) The angle of incidence and the angle of reflection must always be the same. According to the law of reflection, when a wave reflects off a surface, the angle at which it strikes the surface (angle of incidence) is equal to the angle at which it bounces off (angle of reflection). This holds true for all types of surfaces, whether they are smooth or rough.
(d) When two waves cross and their amplitudes add up to create a wave with a larger amplitude than either of the original waves, it is called constructive interference. In constructive interference, the crests of one wave align with the crests of the other wave, resulting in reinforcement and an increase in amplitude. This occurs when the waves are in phase, meaning their peaks and troughs align.
Therefore, the correct answer is: Angle of incidence and angle of reflection must always be the same (a), and when two waves cross and result in a wave with a larger amplitude, it is called constructive interference (d).
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Photons of wavelength 450 nm are incident on a metal. The most energetic electrons ejected from the metal are bent into a circular arc of radius 20.0 cm by a magnetic field with a magnitude of 2.00 x 10^-5 T. What is the work function of the metal?
Photons of wavelength 450 nm are incident on a metal. The most energetic electrons ejected from the metal are bent into a circular arc of radius 20.0 cm by a magnetic field with a magnitude of 2.00 x 10^-5 T.The work function of the metal is approximately 2.45 x 10^-19 J.
To determine the work function of the metal, we can use the relationship between the energy of a photon and the work function of the metal.
The energy of a photon can be calculated using the equation:
E = hc/λ
Where:
E is the energy of the photon,
h is Planck's constant (approximately 6.626 x 10^-34 J·s),
c is the speed of light (approximately 3.00 x 10^8 m/s), and
λ is the wavelength of the photon.
Given that the wavelength of the incident photons is 450 nm (450 x 10^-9 m), we can calculate the energy of each photon.
E = (6.626 x 10^-34 J·s)(3.00 x 10^8 m/s) / (450 x 10^-9 m)
E = 4.42 x 10^-19 J
The energy of each photon is 4.42 x 10^-19 J.
Now, let's consider the electrons being bent into a circular arc by the magnetic field. The centripetal force on the electrons is provided by the magnetic force, given by the equation:
F = q×v×B
Where:
F is the magnetic force,
q is the charge of the electron (approximately -1.60 x 10^-19 C),
v is the velocity of the electrons, and
B is the magnitude of the magnetic field (2.00 x 10^-5 T).
The centripetal force is also given by the equation:
F = mv^2 / r
Where:
m is the mass of the electron (approximately 9.11 x 10^-31 kg), and
r is the radius of the circular arc (20.0 cm or 0.20 m).
Setting these two equations equal to each other and solving for v:
qvB = mv^2 / r
v = qBr / m
Substituting the known values:
v = (-1.60 x 10^-19 C)(2.00 x 10^-5 T)(0.20 m) / (9.11 x 10^-31 kg)
v ≈ -0.704 x 10^6 m/s
The velocity of the electrons is approximately -0.704 x 10^6 m/s.
Now, we can calculate the kinetic energy of the electrons using the equation:
KE = (1/2)mv^2
KE = (1/2)(9.11 x 10^-31 kg)(-0.704 x 10^6 m/s)^2
KE ≈ 2.45 x 10^-19 J
The kinetic energy of the electrons is approximately 2.45 x 10^-19 J.
The work function (Φ) is defined as the minimum energy required to remove an electron from the metal surface. Therefore, the work function is equal to the kinetic energy of the electrons.
Φ = 2.45 x 10^-19 J
Hence, the work function of the metal is approximately 2.45 x 10^-19 J.
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LR.pdf R = 200 H, L=5 mH calulate the cut off frequency Fe Consider the following circuit, L m 7₂ To R = 200 £2, How to choose L if of cut off frequency F=3000Hz
If the cutoff frequency (Fc) is 3000 Hz and the resistance (R) is 200 Ω, the required value of inductance (L) is approximately 1.33 mH.
To calculate the cutoff frequency (Fc) of a circuit with an inductor (L) and a resistor (R), we can use the formula:
Fc = 1 / (2π√(L * R))
Given that R = 200 Ω and Fc = 3000 Hz, we can rearrange the formula to solve for L:
L = (1 / (4π² * Fc² * R))
Substituting the values:
L = (1 / (4π² * (3000 Hz)² * 200 Ω))
L ≈ 1.33 mH
Therefore, if the cutoff frequency (Fc) is 3000 Hz and the resistance (R) is 200 Ω, the required value of inductance (L) is approximately 1.33 mH.
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Light is incident on two slits separated by 0.20 mm. The observing screen is placed 3.0 m from the slits. If the position of the first order bright fringe is at 4.0 mm above the center line, find the wavelength of the light, in nm.
Find the position of the third order bright fringe, in degrees.
Shine red light of wavelength 700.0 nm through a single slit. The light creates a central diffraction peak 6.00 cm wide on a screen 2.40 m away. To what angle do the first order dark fringes correspond, in degrees?
What is the slit width, in m?
What would be the width of the central diffraction peak if violet light of wavelength 440.0 nm is used instead, in cm?
The wavelength of the light is 267 nm, the position of the third order bright fringe is approximately 0.76 degrees, the angle of the first order dark fringe for red light is approximately 0.333 degrees, the slit width is approximately 0.060 m and the width of the central diffraction peak for violet light is approximately 3.8 cm.
To find the wavelength of light, we can use the formula for the position of the bright fringe in a double-slit interference pattern:
y = (m * λ * L) / d
where:
y is the distance of the bright fringe from the center line,
m is the order of the bright fringe (1 for the first order),
λ is the wavelength of light,
L is the distance from the slits to the observing screen,
d is the separation between the two slits.
Given that y = 4.0 mm = 0.004 m, m = 1, L = 3.0 m, and d = 0.20 mm = 0.0002 m, we can solve for λ:
0.004 = (1 * λ * 3.0) / 0.0002
λ = (0.004 * 0.0002) / 3.0 = 2.67 × 1[tex]10^{-7}[/tex] m = 267 nm
Therefore, the wavelength of the light is 267 nm.
To find the position of the third order bright fringe, we can use the same formula with m = 3:
y = (3 * λ * L) / d
Substituting the given values, we have:
y = (3 * 267 * [tex]10^{-9}[/tex] * 3.0) / 0.0002 = 0.040 m
To convert this to degrees, we can use the formula:
θ = arctan(y / L)
θ = arctan(0.040 / 3.0) ≈ 0.76 degrees
Therefore, the position of the third order bright fringe is approximately 0.76 degrees.
For the single-slit diffraction pattern, the formula for the angle of the dark fringe can be expressed as:
θ = λ / (2 * w)
where:
θ is the angle of the dark fringe,
λ is the wavelength of light,
w is the slit width.
Given that λ = 700.0 nm = 7.00 × [tex]10^{-7}[/tex] m and the central diffraction peak width is 6.00 cm = 0.06 m, we can solve for θ:
θ = (7.00 × [tex]10^{-7}[/tex]) / (2 * 0.06) ≈ 0.0058 radians
To convert this to degrees, we multiply by 180/π:
θ ≈ 0.0058 * (180/π) ≈ 0.333 degrees
Therefore, the angle of the first order dark fringe for red light is approximately 0.333 degrees.
To find the slit width w, we rearrange the formula:
w = λ / (2 * θ)
Substituting the given values, we have:
w = (7.00 × [tex]10^{-7}[/tex]) / (2 * 0.0058) ≈ 0.060 m
Therefore, the slit width is approximately 0.060 m.
Finally, to find the width of the central diffraction peak for violet light of wavelength 440.0 nm = 4.40 × [tex]10^{-7}[/tex] m, we can use the same formula:
w = λ / (2 * θ)
Substituting λ = 4.40 × [tex]10^{-7}[/tex] m and θ = 0.0058 radians, we have:
w = (4.40 × [tex]10^{-7}[/tex]) / (2 * 0.0058) ≈ 0.038 m = 3.8 cm
Therefore, the width of the central diffraction peak for violet light is approximately 3.8 cm.
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Three long, parallel wires carry equal currents of I=4.00 A. In a top view, the wires are located at the corners of a square with all currents flowing upward, as shown in the diagram. Determine the magnitude and direction of the magnetic field at a. the empty corner. b. the centre of the square.
(a) The magnitude of the magnetic field at the empty corner is 3π x 10⁻⁷/d, T.
(b) The magnitude of the magnetic field at the center of the square is 0.
What is the magnitude of the magnetic field?(a) The magnitude of the magnetic field at the empty corner is calculated as;
B = μ₀I/2πd
where;
μ₀ is permeability of free spaceI is the currentd is the distance of the wiresThe resultant magnetic field at the empty corner will be the vector sum of the three wire fields:
B_net = 3B
B_net = 3(4π × 10⁻⁷ × 4 / d)
B_net = 3π x 10⁻⁷/d, T
(b) The magnitude of the magnetic field at the center of the square is calculated as;
each magnetic field in opposite direction will cancel out;
B(net) = 0
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Cubic equations of state have proven to be useful for a wide range of compounds and applications in thermodynamics. Explain why we are using cubic equation derived from P vs V data (graph) of liquid and vapor.
Cubic equations of state are highly beneficial for a wide range of thermodynamic applications because they use measurable quantities and provide critical data for predicting phase equilibrium in chemical engineering.
Cubic equations of state are highly useful for a wide range of compounds and applications in thermodynamics. A cubic equation derived from P vs V data (graph) of liquid and vapor is used for a variety of reasons, including: These equations make use of measurable quantities (pressure, temperature, and volume) and are extremely beneficial in the development of a thermodynamic framework for different compounds. These models may be used to estimate properties such as vapor pressures, fugacity coefficients, and liquid molar volumes, among others. The approach also allows for the calculation of the fugacity and molar volume of an ideal gas for a pure substance.
The data provided by these graphs are critical for predicting phase equilibrium in chemical engineering applications. They can also assist in the calculation of mixing and phase separation behavior for a variety of compounds. By using these equations, thermodynamic experts may evaluate the behavior of a substance and its properties under a variety of conditions, which is critical in the design and development of chemical processes. In conclusion, cubic equations of state are highly beneficial for a wide range of thermodynamic applications because they use measurable quantities and provide critical data for predicting phase equilibrium in chemical engineering.
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An electrical circuit contains a capacitor of Z picofarads and a resistor of X ohms. If the x=1503 capacitor is fully charged, and then the voltage is interrupted, in how much time will about 95%Z=15.03 m of its charge be transferred to the resistor? Show your calculations.
The time taken to transfer about 95% of the charge to the resistor is 65.4 s (approx)
The given values in the problem are:X = 1503 ΩZ = 15.03 mF
The time taken to transfer about 95% of its charge to the resistor can be determined using the time constant (τ) of the circuit. The time constant (τ) of the circuit is given by the formula; τ = RC
where R is the resistance of the circuit in ohms and C is the capacitance of the circuit in farads.τ = RC = (1503 Ω)(15.03 × 10⁻³ F) = 22.56849 s ≈ 22.6 s (approx)
After one time constant, the charge on the capacitor is reduced to about 36.8% of its initial charge.
Hence, to transfer about 95% of its charge to the resistor, we need to wait for about 2.9 time constants (95 ÷ 36.8 ≈ 2.9).
The time taken to transfer about 95% of the charge to the resistor is;T = 2.9τ = 2.9 × 22.56849 s = 65.43861 s ≈ 65.4 s (approx)
Therefore, the time taken to transfer about 95% of the charge to the resistor is 65.4 s (approx)
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A modern 1,200 MWe nuclear power station converts thermal energy to electricity via a steam cycle with an efficiency of 33%. Over the year it consumed 25 tonnes of enriched uranium although refuelling and maintenance meant the plant was not generating for a total of 8 weeks. Calculate the average fuel burnup rate in GWd/t.
The average fuel burnup rate in GWd/t is 6,984.
To calculate the average fuel burnup rate in GWd/t, we need to determine the total energy generated by the reactor over the year. The formula for calculating the total energy generated is:
Total energy generated = Annual energy generation / efficiency
Given that the annual energy generation is 1,200 GW and the efficiency is 0.33, we can calculate the total energy generated as follows:
Total energy generated = 1,200 GW x 8,760 hours / 0.33 = 31,891,891 MWh
Next, we need to calculate the mass of uranium consumed by the reactor over a year. The specific energy release for enriched uranium used in a typical modern reactor is approximately 7,000 kWh/kg. Using this value, we can calculate the mass of uranium consumed as follows:
Mass of uranium consumed = Total energy generated / Specific energy release
Mass of uranium consumed = 31,891,891 MWh x 10^6 / (7,000 kWh/kg x 10^3) = 4,560 tonnes
Therefore, the mass of uranium consumed by the reactor over the year is 4,560 tonnes.
The fuel burnup rate is defined as the amount of energy produced per unit mass of fuel consumed. We can calculate the fuel burnup rate as follows:
Fuel burnup rate = Total energy generated / Mass of uranium consumed
Fuel burnup rate = 31,891,891 MWh x 10^6 / (4,560 tonnes x 10^3)
Fuel burnup rate = 6,984 GWd/t
Therefore, the average fuel burnup rate in GWd/t is 6,984.
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"Charging" the magnetic field of an inductor 60.000 m of wire is wound on a cylinder, tight packed and without any overlap, to a diameter of 2.00 cm (relenoid 0.0100 m ). The wire has a radius of rune −0.00100 m and a total resistance of 0.325Ω. This inductor initially has no current flowing in it. It is suddenly connected to a DC voltage source at time t−0.000sec. V s
=2.00Volts. After 2 time constants, the current across the inductor will be.... Hint: first find the inductor currents I t=[infinity]
I F=[infinity]
After 2 time constants, the current across the inductor will be approximately 5.320 Amperes. The current across the inductor after 2 time constants, we need to calculate the time constant and then use it to find the current at that time. The time constant (τ) of an RL circuit (resistor-inductor circuit) is given by the formula:
τ = L / R,
where L is the inductance and R is the resistance.
First, let's calculate the inductance of the coil. The inductance of a tightly packed solenoid can be approximated using the formula:
L = (μ₀ * N² * A) / l,
where μ₀ is the permeability of free space (4π x [tex]10^-7[/tex]T·m/A), N is the number of turns, A is the cross-sectional area of the solenoid, and l is the length of the solenoid.
Number of turns, N = 60,000
Cross-sectional area, A = π * ([tex]0.0200 m)^2[/tex]
Length of the solenoid, l = 0.0100 m
Using these values, we can calculate the inductance:
L = (4π x [tex]10^-7[/tex]T·m/A) * ([tex]60,000 turns)^2[/tex] * (π * [tex](0.0200 m)^2[/tex]) / 0.0100 m
≈ 0.301 T·m²/A
Next, we can calculate the time constant:
τ = L / R = 0.301 T·m²/A / 0.325 Ω
≈ 0.926 s
Now, we can determine the current after 2 time constants:
I(t) = I(∞) * (1 - e^(-t/τ)),
where I(t) is the current at time t, I(∞) is the final current (as t approaches infinity), and e is the base of the natural logarithm.
Since t = 2τ, we can substitute this value into the equation:
I(2τ) = I(∞) * (1 - e^(-2))
≈ I(∞) * (1 - 0.1353)
≈ I(∞) * 0.8647
We are given that the voltage source is 2.00 Volts. Using Ohm's law (V = I(∞) * R), we can solve for I(∞):
2.00 V = I(∞) * 0.325 Ω
I(∞) = 2.00 V / 0.325 Ω
≈ 6.153 A
Finally, we can calculate the current after 2 time constants:
I(2τ) ≈ I(∞) * 0.8647
≈ 6.153 A * 0.8647
≈ 5.320 A
Therefore, after 2 time constants, the current across the inductor will be approximately 5.320 Amperes.
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How do I derive the formula for the magnetic field at a point
near infinite and semi-infinite long wire using biot savart's
law?
To derive the formula for the magnetic field at a point near an infinite and semi-infinite long wire using Biot-Savart's law.
Follow these steps: the variables, Express Biot-Savart's law, the direction of the magnetic field, an infinite long wire and a semi-infinite long wire.
Define the variables:
I: Current flowing through the wire
dl: Infinitesimally small length element along the wire
r: Distance between the point of interest and the current element dl
θ: Angle between the wire and the line connecting the current element to the point of interest
μ₀: Permeability of free space (constant)
Express Biot-Savart's law:
B = (μ₀ / 4π) * (I * dl × r) / r³
This formula represents the magnetic field generated by an infinitesimal current element dl at a distance r from the wire.
Determine the direction of the magnetic field:
The magnetic field is perpendicular to both dl and r, and follows the right-hand rule. It forms concentric circles around the wire.
Consider an infinite long wire:
In the case of an infinite long wire, the wire extends infinitely in both directions. The current is assumed to be uniform throughout the wire.
The contribution to the magnetic field from different segments of the wire cancels out, except for those elements located at the same distance from the point of interest.
By symmetry, the magnitude of the magnetic field at a point near an infinite long wire is given by:
B = (μ₀ * I) / (2π * r)
This formula represents the magnetic field at a point near an infinite long wire.
Consider a semi-infinite long wire:
In the case of a semi-infinite long wire, we have one end of the wire located at the point of interest, and the wire extends infinitely in one direction.
The contribution to the magnetic field from segments of the wire located beyond the point of interest does not affect the field at the point of interest.
By considering only the current elements along the finite portion of the wire, we can derive the formula for the magnetic field at a point near a semi-infinite long wire.
The magnitude of the magnetic field at a point near a semi-infinite long wire is given by:
B = (μ₀ * I) / (2π * r)
This formula is the same as that for an infinite long wire.
By following these steps, we can derive the formula for the magnetic field at a point near an infinite and semi-infinite long wire using Biot-Savart's law.
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A monochromatic source emits a 6.3 mW beam of light of wavelength 600 nm. 1. Calculate the energy of a photon in the beam in eV. 2. Calculate the number of photons emitted by the source in 10 minutes. The beam is now incident on the surface of a metal. The most energetic electron ejected from the metal has an energy of 0.55 eV. 3. Calculate the work function of the metal.
The power emitted by a monochromatic source is 6.3 m Wavelength of light emitted by the source is 600 nm.
1. Energy of photon, E = hc/λ
where, h = Planck's constant = 6.63 × 10⁻³⁴ Js, c = Speed of light = 3 × 10⁸ m/s, λ = wavelength of light= 600 nm = 600 × 10⁻⁹ m
Substitute the values, E = (6.63 × 10⁻³⁴ J.s × 3 × 10⁸ m/s)/(600 × 10⁻⁹ m) = 3.31 × 10⁻¹⁹ J1 eV = 1.6 × 10⁻¹⁹ J
Hence, Energy of photon in eV, E = (3.31 × 10⁻¹⁹ J)/ (1.6 × 10⁻¹⁹ J/eV) = 2.07 eV (approx.)
2. The power is given by,
P = Energy/Time Energy, E = P × Time Where P = 6.3 mW = 6.3 × 10⁻³ W, Time = 10 minutes = 10 × 60 seconds = 600 seconds
E = (6.3 × 10⁻³ W) × (600 s) = 3.78 J
Number of photons emitted, n = E/Energy of each photon = E/E1 = 3.78 J/3.31 × 10⁻¹⁹ J/photon ≈ 1.14 × 10²¹ photons
3. The work function (ϕ) of a metal is the minimum energy required to eject an electron from the metal surface. It is given by the relation, K max = hv - ϕ where Kmax = Maximum kinetic energy of the ejected electron, v = Frequency of the incident radiation (v = c/λ), and h = Planck's constant.
Using Kmax = 0.55 eV = 0.55 × 1.6 × 10⁻¹⁹ J, h = 6.63 × 10⁻³⁴ Js, λ = 600 nm = 600 × 10⁻⁹ m,v = c/λ = 3 × 10⁸ m/s ÷ 600 × 10⁻⁹ m = 5 × 10¹⁴ s⁻¹.
Substituting all the values in the above formula,ϕ = hv - Kmaxϕ = (6.63 × 10⁻³⁴ Js × 5 × 10¹⁴ s⁻¹) - (0.55 × 1.6 × 10⁻¹⁹ J)ϕ ≈ 4.3 × 10⁻¹⁹ J
Therefore, the work function of the metal is approximately equal to 4.3 × 10⁻¹⁹ J.
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The headlamp of a car take a current of 0.4A from a 12 volt the energy produced in 5 minutes is
Answer:
1440 J
Explanation:
Voltage (V) = 12 v
Current (I) = 0.4 A
Time (t) = 5min = 300sec
Power = Voltage x Current;
P = V x I = 12 x 0.4 = 4.8 W
We founded power, so for now we have to find energy. We will use another formula of power:
Power = Energy / Time
For now we will rearange the formula to find energy:
Energy = Power x Time;
E= P x t = 4.8W x 300sec = 1440 J
Consider the following system and its P controller transfer functions, G(s) and Ge(s) respectively: C(s) and G)-Kp=7 5s +1 r(t) e(t) u(t) y(t) Ge(s) G(s) 12.10.2011 10/201 y(t) Find the time constant after adding the controller Ges), for a unit step input. (Note: don't include units in your answer and calculate the answer to two decimal places for example 0.44)
The time constant of the closed-loop system is 1/35, which is approximately equal to 0.03
To find the time constant after adding the controller Ge(s) to the system, we need to determine the transfer function of the closed-loop system. The transfer function of the closed-loop system, T(s), is given by the product of the transfer function of the plant G(s) and the transfer function of the controller Ge(s):
T(s) = G(s) * Ge(s)
In this case, G(s) = 5s + 1 and Ge(s) = Kp = 7.
Substituting these values into the equation, we get:
T(s) = (5s + 1) * 7
= 35s + 7
To find the time constant of the closed-loop system, we need to determine the inverse Laplace transform of T(s).
Taking the inverse Laplace transform of 35s + 7, we obtain:
t(t) = 35 * δ'(t) + 7 * δ(t)
Here, δ(t) is the Dirac delta function, and δ'(t) is its derivative.
The time constant is defined as the reciprocal of the coefficient of the highest derivative term in the expression. In this case, the highest derivative term is δ'(t), and its coefficient is 35. Therefore, the closed-loop system's time constant is 1/35, which is nearly equivalent to 0.03. (rounded to two decimal places).
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High frequency alternating current is passed through a solenoid that contains a solid copper core insulated from the coils of the solenoid. Which statement is correct? O A copper core remains cool no matter what the frequency of the current in the solenoid is. The copper core remains cool because the induced emf is parallel to the solenoid axis and fluctuates rapidly. 0 The copper core heats up because an emf parallel to the solenoid axis is induced in the core. O The copper core heats up because circular currents around its axis are induced in the core. O The copper core heats up because the electric field induced in the copper is parallel to the magnetic field produced by the solenoid.
The correct statement is that c. the copper core heats up because circular currents around its axis are induced in the core.
What is a solenoid?
A solenoid is a long coil of wire with numerous turns that are tightly packed together. It produces a uniform magnetic field when electrical energy is passed through it. An electric current flowing through a solenoid produces a magnetic field that is proportional to the number of turns in the coil and the magnitude of the electric current.
The statement, "The copper core heats up because circular currents around its axis are induced in the core" is correct. The magnetic field produced by the solenoid induces circular currents in the copper core. These circular currents are referred to as eddy currents. The eddy currents heat up the copper core and, as a result, the copper core becomes hot.
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Applications of Electrostatics The electric field one-fourth of the way from a charge 4: to another charge 92 is zero. What is the ratio of 1 to 4z?
The electric field is the area around electrically charged particles where the interaction between them creates an electric force. Electrostatics finds applications in a wide range of areas, including in the following fields:
In the industry, electrostatics is used to eliminate dirt and dust from plastic surfaces before painting them to achieve good adhesion. Aerospace engineering uses electrostatics in applications like the electrostatic cleaning of dust from the surface of spacecraft or the charging of space probes and dust detectors.
Medical technology relies on electrostatics in a range of applications, including in electrocardiography, electrophoresis, and in the use of electrostatic precipitators for respiratory protection.The electric field one-fourth of the way from a charge 4 to another charge 92 is zero.
What is the ratio of 1 to 4z?
The distance between charge 4 and charge 92 is 4z. Therefore, we can say that the electric field is zero at a distance of z from charge 4 (since z is 1/4th of the distance between 4 and 92).
Using Coulomb's law, we can calculate the electric field as:
E = (kQq)/r² Where k is the Coulomb constant, Q and q are the magnitudes of the charges, and r is the distance between them.
Since the electric field is zero at a distance of z from charge 4, we can write:
(k*4*Q)/(z²) = 0
Solving for Q, we get:
Q = 0
Therefore, the ratio of 1 to 4z is: 1/4z = 1/(4*z) = (1/4) * (1/z) = 0.25z^-1
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What is the pressure inside a 32.0 L container holding 104.1 kg of argon gas at 20.3°C?
The pressure inside the 32.0 L container holding 104.1 kg of argon gas at 20.3°C is approximately 67279.93 Pa.
To calculate the pressure inside a container of gas, we can use the ideal gas law equation:
PV = nRT
Where:
P is the pressure of the gas
V is the volume of the container
n is the number of moles of gas
R is the ideal gas constant (8.314 J/(mol·K))
T is the temperature in Kelvin
First, let's convert the given temperature from Celsius to Kelvin:
T = 20.3°C + 273.15 = 293.45 K
Next, we need to determine the number of moles of argon gas using the molar mass of argon (Ar), which is approximately 39.95 g/mol.
n = mass / molar mass
n = 104.1 kg / (39.95 g/mol * 0.001 kg/g)
n = 2604.006 moles
Now, we can substitute the values into the ideal gas law equation to solve for the pressure:
P * 32.0 L = (2604.006 mol) * (8.314 J/(mol·K)) * 293.45 K
P = (2604.006 * 8.314 * 293.45) / 32.0
P ≈ 67279.93 Pa
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15.4 cm. Given this wavelength and frequency, what is the speed of the sound wave? 48.7 cm. Given this wavelength and frequency, what is the speed of the sound wave? speed of sound (in m/s ) under these conditions? Give your answer to the nearest 1 m/s.
Given this wavelength and frequency. that the frequency of the first scenario is approximately 3.168 times the frequency of the second scenario.
To calculate the speed of a sound wave, we can use the formula: speed = wavelength × frequency.
For the first scenario with a wavelength of 15.4 cm, we need to convert it to meters by dividing it by 100: 15.4 cm = 0.154 m. Let's assume a frequency of f1. Using the formula, we have speed = 0.154 m × f1.
For the second scenario with a wavelength of 48.7 cm, we again convert it to meters: 48.7 cm = 0.487 m. Let's assume a frequency of f2. Using the formula, we have speed = 0.487 m × f2.
Since the speed of sound in air is generally considered constant (at approximately 343 m/s at room temperature and normal atmospheric conditions), we can equate the two expressions for speed and solve for f1 and f2
0.154 m × f1 = 0.487 m × f2
By canceling out the common factor of 0.154, we get:
f1 = 0.487 m × f2 / 0.154 m
Simplifying further:
f1 ≈ 3.168 × f2
This equation implies that the frequency of the first scenario is approximately 3.168 times the frequency of the second scenario. Therefore, to determine the speed of sound under these conditions, we need more information about either the frequency in one of the scenarios or the specific speed of sound for the given conditions.
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True or false: A. Hot objects are bluer than cold objects B.The radius of the 3M orbit of Helium is bigger than 10th orbit of Boron (single electron atoms) C. If you raise the temperature of a block body by a factor of 3 is it 9 times brighter D. decay involves a position E. decay shows that there are only some allowed electron orbits in an atom F. decay happens when a proton tums into a neutron G. decay involves a Helium nucleus
Answer: A. False B. True C. True D. False E. False F. False G. True
Explanation:
A. False: Hot objects are not bluer than cold objects. Hot objects actually glow red, yellow or blue, depending on how hot they are.
B. True: As the radius of an electron orbit in an atom is proportional to n2, the radius of the 3M orbit of Helium (n = 3) is greater than the radius of the 10th orbit of Boron (n = 10).
C. True: If we increase the temperature of a body by a factor of 3, the power of emitted radiation increases by 34 or 81. Therefore, the brightness increases by a factor of 81.
D. False: Decay does not involve a position.
E. False: Decay does not show that there are only some allowed electron orbits in an atom.
F. False: Decay does not happen when a proton turns into a neutron.
G. True: Alpha decay, also known as decay, is the process in which a Helium nucleus is emitted.
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A tunesten light bulb filament may operate at 3200 K. What is its Fahrenhelt temperature? ∘
F
The Fahrenheit temperature of a tungsten light bulb filament operating at 3200 K is approximately 5476 °F.
To convert the temperature from Kelvin (K) to Fahrenheit (°F), we can use the following formula:
°F = (K - 273.15) * 9/5 + 32
Substituting the given temperature of 3200 K into the formula, we have:
°F = (3200 - 273.15) * 9/5 + 32
Simplifying the equation, we get:
°F = (2926.85) * 9/5 + 32
°F ≈ 5476 °F
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1. An car’s engine idles at 1200 rpm. Determine the
frequency in hertz. 2. What would be the frequency of a space-station
spinning at 120o per second?
The car engine idling at 1200 rpm has a frequency of 20 Hz. The space-station spinning at 120 degrees per second has a frequency of approximately 0.333 Hz.
To determine the frequency in hertz, we need to convert the rotations per minute (rpm) to rotations per second. We can use the following formula:
Frequency (in hertz) = RPM / 60
For the car engine idling at 1200 rpm:
Frequency = 1200 / 60 = 20 hertz
For the space-station spinning at 120 degrees per second, we need to convert the degrees to rotations before calculating the frequency. Since one complete rotation is equal to 360 degrees, we can use the following formula:
Frequency (in hertz) = Rotations per second = Degrees per second / 360
For the space-station spinning at 120 degrees per second:
Frequency = 120 / 360 = 1/3 hertz or approximately 0.333 hertz
Therefore, the frequency of the car engine idling at 1200 rpm is 20 hertz, while the frequency of the space-station spinning at 120 degrees per second is approximately 0.333 hertz.
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A Carnot refrigeration cycle is used to maintain a room at
23 °C by removing heat from groundwater at 15 °C.
Refrigerant R-134a enters the condenser as saturated
vapor at 40 °C and leaves as saturated liquid at the
same temperature. The evaporator pressure is 351 kPa.
a) If the room is to receive 2kW, what is power input to
the compressor?
b) Net power input to cycle?
a) The power input to the compressor in the Carnot refrigeration cycle, in order to supply 2 kW of cooling to the room, will depend on the efficiency of the cycle and the heat transfer involved.
b) The net power input to the cycle can be determined by considering the work done by the compressor and the work done on the system.
a) To calculate the power input to the compressor, we need to determine the heat transfer from the groundwater to the room. The Carnot refrigeration cycle is an idealized cycle, and its efficiency is given by the equation: Efficiency = 1 - (T_evaporator / T_condenser), where T_evaporator and T_condenser are the temperatures at the evaporator and condenser, respectively. Using this efficiency, we can calculate the heat transfer from the groundwater and convert it to power input.
b) The net power input to the cycle takes into account the work done by the compressor and the work done on the system. It can be calculated by subtracting the work done by the compressor from the heat transfer from the groundwater. The work done by the compressor can be determined using the power input calculated in part a), and the heat transfer from the groundwater can be obtained using the given temperatures and the specific heat properties of the refrigerant.
Overall, the Carnot refrigeration cycle involves several calculations to determine the power input to the compressor and the net power input to the cycle, considering the heat transfer and work done in the system.
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In the above figure you have five charges equally spaced from O. Therefore at the point O a. What is the net vertical electric field? (3) b. What is the net horizontal electric field? (4) c. What is the potential V?(4) d. If I place a 2C charge at O, what is the magnitude and the direction of the force it will experience? (2) e. What will be the potential energy of this 2C charge?
The potential energy of this 2C charge is equal to the work required to bring it from infinity to the point O. Since the potential at infinity is zero, the potential energy of the 2C charge at O is also zero.
a. The net vertical electric field at the point O is zero. There are two negative and two positive charges, with symmetrical arrangements, and so, the electric fields at O add up to zero.b.
The net horizontal electric field at the point O is zero. There are two negative and two positive charges, with symmetrical arrangements, and so, the electric fields at O add up to zero. c. The potential V at point O is zero. The potential at any point due to these charges is calculated by adding the potentials at that point due to each of the charges.
For symmetrical arrangements like the present one, the potential difference at O due to each charge is equal and opposite, and so, the potential difference due to the charges at O is zero. d. If a 2C charge is placed at O, it will experience a net force due to the charges on either side of O.
The magnitudes of these two forces will be equal and the direction of each of these forces will be towards the other charge. The two forces will add up to give a net force of magnitude F = kqQ/r^2, where k is the Coulomb constant, q is the charge at O, Q is the charge to either side of O, and r is the separation between the two charges.e.
The potential energy of this 2C charge is equal to the work required to bring it from infinity to the point O. Since the potential at infinity is zero, the potential energy of the 2C charge at O is also zero.
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Consider an electric field perpendicular to a work bench. When a small charged object of mass 4.00 g and charge -19.5 μC is carefully placed in the field, the object is in static equilibrium. What are the magnitude and direction of the electric field? (Give the magnitude in N/C.) magnitude N/C direction
The magnitude of the electric field is 5.12 × 10^6 N/C, and it is directed upwards.
In order for the charged object to be in static equilibrium, the electric force acting on it must balance the gravitational force. The electric force experienced by the object can be calculated using the equation F = qE, where F is the force, q is the charge of the object, and E is the electric field.
Given that the mass of the object is 4.00 g (or 0.004 kg) and the charge is -19.5 μC (or -1.95 × [tex]10^{-8}[/tex] C), we can calculate the gravitational force acting on the object using the equation F_gravity = mg, where g is the acceleration due to gravity (approximately 9.8 [tex]m/s^2[/tex]).
Since the object is in equilibrium, the electric force and the gravitational force are equal in magnitude but opposite in direction. Therefore, we have F = F_gravity. Substituting the values, we get qE = mg, which can be rearranged to solve for the electric field E.
Plugging in the known values, we have (-1.95 × [tex]10^{-8}[/tex] C)E = (0.004 kg)(9.8 [tex]m/s^2[/tex]). Solving for E gives us E = (0.004 kg)(9.8 [tex]m/s^2[/tex])/(-1.95 × [tex]10^-8[/tex] C) ≈ 5.12 × [tex]10^6[/tex] N/C.
The negative charge on the object indicates that the direction of the electric field is directed upwards, opposite to the direction of the gravitational force.
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Question 5 (2 points) Listen Which of the following best describes the image produced by a flat mirror? real, inverted, and magnification less than one virtual, inverted, and magnification greater than one virtual, upright, and magnification equal to one real, upright, and magnification equal to one
The best description of the image produced by a flat mirror is: virtual, upright, and magnification equal to one. In the case of a flat mirror, the image formed is virtual, which means it cannot be projected onto a screen.
Instead, the image is formed by the apparent intersection of the reflected rays. This virtual image is always located behind the mirror, at the same distance as the object, and it cannot be physically captured or projected.
Furthermore, the image formed by a flat mirror is upright, meaning it has the same orientation as the object. If you raise your right hand in front of a flat mirror, the image in the mirror will also show a raised right hand. The mirror preserves the direction of the light rays, resulting in an upright image.
Lastly, the magnification of a flat mirror is equal to one. Magnification refers to the ratio of the height of the image to the height of the object. Since the image formed by a flat mirror is the same size as the object, the magnification is equal to one.
To summarize, a flat mirror produces a virtual, upright image with a magnification equal to one. It reflects the light rays without altering their orientation or size, allowing us to see ourselves and objects with a preserved reflection.
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A 6 pole induction motor has the ratings: U₁ = 400 V, n = 970 rpm, ƒ№ = 50 Hz, the stator windings are connected as Y, if the parameters are: r₁ = 2.08 №, r₂ = 1.53 N, x₁ = 3.12 №, x₂ = 4.25 N. Find out: (a) rated slip; (b) maximum torque; (c) overload ability Ami (d) the slip when the maximum torque occurs.
The maximum torque is 1082 Nm, which is achieved at 6.5% slip. The overload capacity is 227%. is the answer.
A 6-pole induction motor has the following specifications: U1 = 400 V, n = 970 rpm, f1 = 50 Hz, and the stator windings are connected in Y. Given the parameters r1 = 2.08 Ω, r2 = 1.53 Ω, x1 = 3.12 Ω, and x2 = 4.25 Ω, we are required to find out the following: rated slip maximum torque overload capacity
The formula for slip (s) is given by: s = (ns - nr) / ns where ns = synchronous speed
nr = rotor speed
Using the given values, we get: s = (ns - nr) / ns= (120 * f1 - nr) / (120 * f1)= (120 * 50 - 970) / (120 * 50)= 0.035 or 3.5%
This is the rated slip.
Maximum torque is achieved at the slip (s) that is 0.1 to 0.15 less than the rated slip (sr).
Hence, maximum torque slip (sm) can be calculated as follows: sm = sr - 0.1sr = rated slip sm = sr - 0.1= 0.035 - 0.1= -0.065or 6.5% (Approx)
The maximum torque is given by: T max = 3V12 / (2πf1) * (r2 / s) * [(s * (r2 / s) + x2) / ((r1 + r2 / s)2 + (x1 + x2)2) + s * (r2 / s) / ((r2 / s)2 + x2)2] where,V1 = 400 Vr1 = 2.08 Ωr2 = 1.53 Ωx1 = 3.12 Ωx2 = 4.25 Ωf1 = 50 Hz s = 0.035 (Rated Slip)
Putting all the values in the formula, we get: T max = 3 * 4002 / (2π * 50) * (1.53 / 0.035) * [(0.035 * (1.53 / 0.035) + 4.25) / ((2.08 + 1.53 / 0.035)2 + (3.12 + 4.25)2) + 0.035 * (1.53 / 0.035) / ((1.53 / 0.035)2 + 4.25)2]= 1082 Nm
Overload capacity is the percentage of the maximum torque that the motor can carry continuously.
This can be calculated using the following formula: Am = Tmax / Tn where T max = 1082 Nm
Tn = (2 * π * f1 * n) / 60 (Torque at rated speed)Putting all the values, we get: Am = Tmax / Tn= 1082 / [(2 * π * 50 * 970) / 60]= 2.27 or 227%
Therefore, the rated slip is 3.5%.
The maximum torque is 1082 Nm, which is achieved at 6.5% slip. The overload capacity is 227%.
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A 97 kg person receives a whole-body radiation dose of 1.9 x 10⁻⁴Gy, delivered by alpha particles for which the RBE factor is 13. Calculate (a) the absorbed energy and the dose equivalent in (b) sieverts and (c) rem.
(a) Number ____________ Units ____________
(b) Number ____________ Units ____________
(c) Number ____________ Units ____________
(a) The number of absorbed energy is calculated to be 0.24033 J. The units for absorbed energy are joules (J). (b) The dose equivalent is calculated to be 0.00247 Sv. The units for dose equivalent are sieverts (Sv). (c) The dose equivalent in rem is 0.247 rem. The units for dose equivalent in rem is rem.
(a) The absorbed energy can be calculated by multiplying the absorbed dose, RBE factor, and mass of the person. In this case, the absorbed energy is found to be 0.24033 J.
(b) The dose equivalent is obtained by multiplying the absorbed dose and the quality factor. For alpha radiation, the quality factor is 13. Thus, the dose equivalent is calculated as 0.00247 Sv.
(c) The dose equivalent in rem is derived by converting Sv to rem. To convert, the dose equivalent in Sv is multiplied by 100. Therefore, the dose equivalent in rem is found to be 0.247 rem.
In summary, the absorbed energy is 0.24033 J, the dose equivalent is 0.00247 Sv, and the dose equivalent in rem is 0.247 rem.
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(a) How many minutes does it take a photon to travel from the Sun to the Earth? imin (b) What is the energy in eV of a photon with a wavelength of 513 nm ? eV (c) What is the wavelength (in m ) of a photon with an energy of 1.58eV ? m
(a) It takes approximately 8.3 minutes for a photon to travel from the Sun to the Earth.
(b) A photon with a wavelength of 513 nm has an energy of approximately 2.42 eV.
(c) A photon with an energy of 1.58 eV has a wavelength of approximately 7.83 × 10^-7 meters.
(a) Calculation of the time it takes a photon to travel from the Sun to the Earth:
The average distance from the Sun to the Earth is approximately 93 million miles or 150 million kilometers. Convert this distance to meters by multiplying it by 1,000, as there are 1,000 meters in a kilometer. So, the distance is 150,000,000,000 meters.
The speed of light in a vacuum is approximately 299,792 kilometers per second or 299,792,458 meters per second. To find the time it takes for a photon to travel from the Sun to the Earth, divide the distance by the speed of light:
Time = Distance / Speed of Light
Time = 150,000,000,000 meters / 299,792,458 meters per second
This gives approximately 499.004 seconds. To convert this to minutes, we divide by 60:
Time in minutes = 499.004 seconds / 60 = 8.3167 minutes
Therefore, it takes approximately 8.3 minutes for a photon to travel from the Sun to the Earth.
(b) Calculation of the energy of a photon with a wavelength of 513 nm:
The energy of a photon can be calculated using the equation E = hc/λ, where E is the energy, h is Planck's constant, c is the speed of light, and λ is the wavelength of the photon.
Planck's constant (h) is approximately 4.1357 × 10^-15 eV·s.
The speed of light (c) is approximately 299,792,458 meters per second.
The given wavelength is 513 nm, which can be converted to meters by multiplying by 10^-9 since there are 1 billion nanometers in a meter. So, the wavelength is 513 × 10^-9 meters.
Substituting the values into the equation,
E = (4.1357 × 10^-15 eV·s × 299,792,458 m/s) / (513 × 10^-9 m)
Simplifying the equation, we get:
E = (1.2457 × 10^-6 eV·m) / (513 × 10^-9 m)
By dividing the numerator by the denominator,
E ≈ 2.42 eV
Therefore, a photon with a wavelength of 513 nm has an energy of approximately 2.42 eV.
(c) Calculation of the wavelength of a photon with an energy of 1.58 eV:
To find the wavelength of a photon given its energy, we rearrange the equation E = hc/λ to solve for λ.
We have the given energy as 1.58 eV.
Substituting the values into the equation,
1.58 eV = (4.1357 × 10^-15 eV·s × 299,792,458 m/s) / λ
To isolate λ, we rearrange the equation:
λ = (4.1357 × 10^-15 eV·s × 299,792,458 m/s) / 1.58 eV
By dividing the numerator by the denominator,
λ ≈ 7.83 × 10^-7 meters
Therefore, a photon with an energy of 1.58 eV has a wavelength of approximately 7.83 × 10^-7 meters or 783 nm.
These calculations assume that the photons are traveling in a vacuum.
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