From the activity values and the decay constant, the mass of of Strontium in the sample is:
[tex]1.62 × 10^{-7}g[/tex]
What is the decay constant of an element?The decay constant of an element is the probability of decay of a nucleus per unit time.
{λ = ln 2 / t1/2
where;
t1/2 is the half-life of the isotope.
The half-life is converted to seconds since the decay constant is asked in per seconds.
[tex]28.8 years = 28.8 × 3.156 × 10^{7} = 908928000 s \\ [/tex]
Hence;
[tex]λ = \frac{ln2}{90892800s} = 7.626 s^{-1}[/tex]
The activity of the element, A, the decay constant, λ and the number of nuclei, N are related as follows:
A = (–) λN[tex]N = \frac{8.25 ×10^{5}}{7.626×10^{-10}} = 1.082 × 10^{15} [/tex]
Molar mass of Strontium-90 is 90 g.
1 mole of Strontium-90 contains 6.02×10^23 nuclei.
The mass, m of Strontium in the sample is calculated:
[tex]m = 1.082 × 10^{15} × \frac{90 g}{6.02 × 10^{23}} = 1.62 × 10^{-7}g \\ [/tex]
Therefore, the mass of of Strontium in the sample is:
[tex]1.62 × 10^{-7} \: g[/tex]
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The figure shows the electric field inside a cylinder of radius R= 3.2 mm. The field strength is increasing with time as E= 1.4 ×108t2V/m, where t is in s. The electric field outside the cylinder is always zero, and the field inside the cylinder was zero for t<0. Find an expression for magnetic field strength as a function of time at a distance r>R from the center.
The Magnetic field strength as a function of time will be 2.4 ×10⁻¹¹ T.it is denoted by B.
What is magnetic field strength?The number of magnetic flux lines on a unit area passing perpendicular to the given line direction is known as induced magnetic field strength
Given
The radius of cylinder is,R=2.8 mm = 0.028 m
[tex]\rm \oint B.ds = \frac{\mu_0 \epsilon_0 d\phi}{dt} \\\\ B \times 2\pi r = \frac{\mu_0 \EPSILON_0 d (EA)i}{dt} \\\\\ b = \frac{\mu_0 \epsilon_0 \times \PI r^ 2 d(E)}{dt} \times \frac{1}{2\pir} \\\\ B= \frac{\mu_0 \epsilon_0 \times rd (E)}{2dt} \\\\ B= \frac{1.26 \times 10^{-5}\times 8.85 \times 10^{-12}\times (3.2 \times 10^{-3})\times 1.4 \times 10^8}{2} \\\\ B =2.4 \times 10^{-11} \ T[/tex]
Hence, magnetic field strength as a function of time will be 2.4 ×10⁻¹¹ T.
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29. All living organisms contain carbon. As organisms grow, they require
large quantities of carbon to carry out life processes and make new cells.
Where is the source of most of Earth's available carbon?
A. New carbon atoms are constantly being created by the process of
photosynthesis.
B. Carbon atoms are constantly transferred from the Sun to Earth along
with sunlight
C. Carbon is constantly transported from the mantle to the crust by volcanic
eruptions.
D. Carbon is constantly recycled from dead organisms back into the
environment.
Answer:
The answer will be D/ Carbon is constantly recycled from dead organisms back into the
environment.
The source of most of Earth's available carbon is: carbon is constantly recycled from dead organisms back into the environment. Hence, option (D) is correct.
What is carbon cycle?The carbon cycle is the exchange of carbon compounds between the earth's biosphere, geosphere, pedosphere, hydrosphere, and atmosphere.
The following are the major steps in the carbon cycle process:
Plants absorb carbon from the atmosphere in order to perform photosynthesis.Animals consume these plants, and carbon is bioaccumulated in their bodies.When these animals and plants die, carbon is released back into the atmosphere as they decompose.Some of the carbon that is not re-emitted into the atmosphere is converted into fossil fuels.These fossil fuels are then used for man-made activities that release additional carbon into the atmosphere.Learn more about carbon cycle here:
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The fundamental frequency of a musical note is 330Hz. Which harmonic is this?
Answer:
it is a type of even harmonic
what is the type of energy possessed by moving water?
Answer:
hydro energy.
Explanation:
The energy possessed by fast-moving water is called hydro energy
What is magnestism? Explain
Answer:
a physical phenomenon produced by the motion of electric charge, which results in attractive and repulsive forces between objects.the ability to attract and charm people.Answer:
Magnetism is the force of attraction or repulsion between substances.
Magnetism is defined as an attractive and repulsive phenomenon produced by a moving electric charge. The affected region around a moving charge consists of both an electric field and a magnetic field. The most familiar example of magnetism is a bar magnet, which is attracted to a magnetic field and can attract or repel other magnets.Magnetism is caused by the electromagnetic force, which is one of the four fundamental forces of nature. Any moving electric charge (electric current) generates a magnetic field perpendicular to it.
two thin lenses of focal length 10cm and 20cm are placed in contract calculate the effective power of the combination
Answer:
20/3
Explanation:
We can use the formula : 1/R1 + 1/R2 = 1/f here
Therefore 1/10 + 1/20 = 3/20
And as it is 1/f its reciprocal will be 20/3
Part 1
An engine absorbs 1969 J from a hot reservoir and expels 1223 J to a cold reservoir in each cycle. What is the engine’s efficiency? Answer with an efficiency in decimal form.
Part 2
How much work is done in each cycle?
Answer in units of J.
Part 3
What is the mechanical power output of the engine if each cycle lasts for 0.345 s?
Answer in units of kW
Answer:
Part 1: 0.3789
Part 2: 746 J
Part 3: 2.162 kW
Explanation:
Part 1:
Eff= [tex]1-\frac{1223}{1969}[/tex]
Eff= 0.378873 ≈ 0/3789
Part 2:
W= 0.3789(1969)
W= 746 J
Part 3:
[tex]Power=\frac{W}{t}[/tex]
[tex]Power= \frac{746}{0.345}[/tex]
Power= 2162.3188 Watts
2162.3188 W-----> 2.162 kW
According to Dr. Ridel's Levels of Critical Thinking in Chapter 1, what level of critical thinking applies to your current status?
The levels of critical thinking classify people into six categories depending on their ability to reflect.
What is critical thinking?This refers to the ability to analyze information, situations, etc. as well as apply, synthesize or evaluate the information learned.
What are the levels?According to Dr. Ridel, the levels are:
Unreflective thinking: They do not reflect on information and lack the skills to have critical thinking.Challenged thinker: This person knows critical thinking is important but has difficulties to have critical thinking.Practicing thinker: This person has better-thinking abilities.Advanced thinker: This person can critically think and has the skills to improve this process.Master thinker: This person is in control of this process and shows superior thinking abilities.Learn more about critical thinking in: https://brainly.com/question/12980631
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The chart shows data for four moving objects.
Object
Initial Velocity
Final Velocity
Change in
(m/s)
(m/s)
Time (s)
29
6
X>N
10
34
12
12
40
20
28
8
Which object has the greatest acceleration?
W
x
Y
Z
Answer:
Explanation:
The chart shows data for four moving objects.
Object
Initial Velocity
Final Velocity
Change in
(m/s)
(m/s)
Time (s)
29
6
X>N
10
34
12
12
40
20
28
8
Which object has the greatest acceleration?
W
x
Y
What scientific process would you be using as you identified the characteristics of the buttery
and leaves?
Answer:
The butterfly and moth develop through a process called metamorphosis.
Explanation:
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Steve is given extra chores each time he hits his little brother. After a few times of having extra chores given to him, Steve's misbehavior toward his little brother decreases. This is an example of __________
Steve's misbehavior toward his little brother decreases. This is an example of Positive punishment
What is positive punishment?
Positive punishment is a variation is a conditioning theory. Its major goal is to minimize future behavior frequency by delivering an unpleasant stimulation after the action has occurred.
Steve is given extra chores each time he hits his little brother. After a few times of having extra chores given to him.
Steve's misbehavior toward his little brother decreases. This is an example of Positive punishment.
Hence positive punishment is the right answer.
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15. A puck is set in motion across a frozen pond. Friction and air resistance may be neglected. If you see the puck change its direction but not its speed, then the
force on the puck is
OA Non-zero, and equal to the product of its mass times its weight
OB. Non-zero, and equal to its weight
OC. Zero
OD. Non-zero, and depends on the puck's new direction
Reset Section
Answer:
the answer is equal to non zero
derive an expression to show tha v=✓2Gr
Answer:
From this equation, it can be said that the escape velocity depends on the radius of the planet and the mass of the planet only and not on the mass of the body. Escape Velocity of Earth= 11.2 km/s. This was the derivation of the escape velocity of earth or any other planet.
Explanation:
What is the surface area of the right cone below?
OA. 63 units²
15
OB. 99 units²
O C. 126 units²
13
OD. 54 units²
Answer:
option d is the answer of given statement
The surface area of the right cone is 54π units². Hence option D correct.
What is Surface Area ?The surface area of a solid object is a total area measured that the surface of the object occupies. the surface area of the cube is 6 times side², cause it has 6 faces.
The surface area is total area occupied by the surface of the object.
A cone is geometrical shape which is having circular base and cone shaped body. when a line is drawn from tip to the center of the base it will make right angle between radius and height of the cone. We can apply Pythagoras theorem to get values of radius, height and hypotenuse.
The total area of the cone is nothing but area of the base plus curved area of the body.
Hence area of the cone is,
A = πr²+πr[tex]\sqrt[]{r^{2}+h^{2} }[/tex]
Given,
r = 3
hypotenuse = [tex]\sqrt[]{r^{2}+h^{2} }[/tex] = 15
A = ?
A = π3²+π3*15
A = π (9+45)
A = 54π units²
Hence area of the cone is 54π units².
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name some factors that would increase braking distance with word not calculation
Which parts of an X-ray image appear white because few X-rays reach the
detector?
A. Those that show where tissues transmitted the most X-rays
B. Those that show where tissues refracted the most X-rays
O C. Those that show where tissues reflected the most X-rays
D. Those that show where tissues absorbed the most X-rays
Answer:
D
Explanation:
Those that show where tissues absorbed the most X-rays.
A net force of 24 N is acting on a 4.0-kg object. Find the acceleration in m/s2.
Hi there!
We can use Newton's Second Law:
[tex]\Sigma F = ma[/tex]
ΣF = Net force (N)
m = mass (kg)
a = acceleration (m/s²)
We can rearrange the equation to solve for the acceleration.
[tex]a = \frac{\Sigma F}{m}\\\\a = \frac{24}{4} = \boxed{6 \frac{m}{s^2}}[/tex]
The figure shows the cross section of a long cylindrical wire of
radius aa, which carries a uniform current ii0. Determine the module of the field
magnetic produced by the current at a distance from the axis of the wire equal to (a)
0, (b) a/2, (c) a (wire surface) and (d) 2a.
Hi there!
Recall Ampere's Law:
[tex]\oint B \cdot dl = \mu_0 i_{encl}[/tex]
B = Magnetic Field Strength (T)
μ₀ = Permeability of Free Space (Tm/A)
i = Enclosed Current (A)
dL = differential path length
To begin, we must derive an expression for the magnetic field strength inside a wire that contains a uniformly-distributed current.
Using the expression:
[tex]i = \int J \cdot dA[/tex]
Where 'J' is the density of current, and A is the cross-sectional area:
[tex]A = \pi r^2\\\\dA = 2\pi r dr[/tex]
We know that:
[tex]J = \frac{i_0 }{A}\\\\J = \frac{i_0}{\pi a^2}[/tex]
This is the current density. We can now integrate:
[tex]i = \int\limits^r_0 {\frac{i_0}{\pi a^2} \cdot 2\pi r} \, dr\\ \\i =\frac{i_0}{a^2}\int\limits^r_0 {2r } \, dr\\\\i = \frac{i_0}{a^2} \cdot r^2 = \frac{i_0 r^2}{a^2}[/tex]
Now, substitute this expression back into the above equation for the magnetic field:
[tex]\oint B \cdot dl = \mu _0 \frac{i_0r^2}{a^2}[/tex]
The path of integration is a closed loop of length 2πr, so:
[tex]B \cdot 2\pi r = \mu_0 \frac{i_0r^2}{a^2}\\\\B = \frac{\mu_0 i_0r}{2\pi a^2}[/tex]
We can now use this equation for the first 2 parts.
a)
If 'r' equals 0:
[tex]B = \frac{\mu _0 i_0 (0)}{2\pi a^2} = \boxed{0 T}[/tex]
b)
If 'r' equals a/2:
[tex]B = \frac{\mu _0 i_0 (\frac{a}{2})}{2\pi a^2} =B =\boxed{ \frac{\mu _0 i_0 }{4\pi a} T}[/tex]
c)
At the wire's surface, 'r' = a:
[tex]B = \frac{\mu _0 i_0 (a)}{2\pi a^2} =B =\boxed{ \frac{\mu _0 i_0 }{2\pi a} T}[/tex]
d)
At 'r' = 2a, since this is outside of the wire, the relationship between magnetic field and distance from the wire becomes a 1/r (inverse) relationship. This is found using Ampere's Law:
[tex]B = \frac{\mu_0 i_0}{2\pi r}\\[/tex]
[tex]B = \frac{\mu_0 i_0}{2\pi (2a)} \\\\\boxed{B = \frac{\mu_0 i_0}{4\pi a}\\}[/tex]
Weather hazards and natural disasters such as tsunamis, earthquakes, and flooding are considered which type of migration factor?
A. Pull factor
B. Both push and pull factors
C. Neither push or pull factor
D. Push factor
Answer:
D. Push Factor
Explanation:
Pull factors are known as positive aspects of a place that make people want to stay/remain in that area.Push factors are known as negative aspects of a place that make people want to leave/depart from that area.Weather hazards and natural disasters are horrendously negative things that people actively seek to avoid; they make people want to leave or depart from an area in order to escape them. As such, they are considered push factors.
(Weather hazards and natural disasters are not pull factors because when discussing push vs pull we are specifically describing the mentioned factor. This aspect is not considered both because the migration factor mentioned in this question actively makes people want to move to any area that avoids their issue. Remember that pull factors make people want to move to a specific place for a unique advantage, while push factors make people want to move to any general place for a common advantage.)
a rescue diver of mass 89 kg jumps from a hovering helicopter into the ocean below, what is the diver's speed (in m/s) when he hits the water
Answer:
Need the HEIGHT of the helicopter to complete this answer
Explanation:
PE (=mgh) is converted to KE ( = 1/2 mv^2 )
mgh = 1/2 m v^2
gh = 1/2 v^2
v^2 = 2 gh
v = sqrt (2gh) = sqrt ( 2 * 9.8 * h)
what are two ways an object can gain more gravitational potential energy?
When an item is raised, the work is done in opposition to gravity. When an item is worked on, energy is transmitted to it, and it develops gravitational potential energy. If the same thing falls from that height, gravity must do the same amount of effort to bring it back to the Earth's surface.
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The speed of light is 300,000,000 m/s. What is the frequency of microwaves with a wavelength of 0.01 meter?
Answer:
c = 3.00E8 m/s speed of light
c = f * λ frequency ^ wavelength
f = c / λ = 3.00E8 m/s / .01 m = 3.00E10 / sec
f = 30,000,000,000 /sec
What role does friction play in the conservation of enérgy?
The law of conservation of energy asserts that total energy remains constant in an isolated system. That is, energy cannot be generated or destroyed, but it may be transferred from one form to another. Frictional forces can dissipate energy, which raises the question of whether it violates the law of conservation of energy. No, it does not. When there is friction, energy is transferred from one form to another. There will be no energy loss. To illustrate this issue, consider the following scenario: two buses collide. The buses are no longer moving as a result of the collision. Where does all of this energy go? The solution is simple: the friction between buses and between buses and the road allows energy to be transferred from one form to another. You may be aware that when we rub our hands together, heat is produced; what occurs here is frictional energy converting to heat energy. This is what happens in bus accidents, where the energies can be changed to thermal energy, acoustic energy, or any other type of energy owing to friction and impact. So the energy we believed we had wasted was really converted to heat and sound. Bus collisions are not only noisy, but they also cause a lot of friction on the ground and in the bent metal. Both heat and sound are types of energy.
NOTE:Styrofoam holds onto its electrons because is has a high _____ for them.
a
polarization
b
affinity
c
insulator
d
conductor
Answer:
Polarization
Explanation:
Obviously, B wouldn't be it as objects don't have feelings. C, and D wouldn't be it also because the grammar of it doesn't fit.
What is the entropy change when 2 g of water changes from 0 °C to steam at 234 °C if (The thermal capacity is pressure) Cp = 1 J / kg.K and a latent heat of vaporization is 54 J/Kg?
Answer:
[tex] \boxed{ \sf \: \Delta S = 0.219J /K}[/tex]
Explanation:
Given:
mass of substance (water) = 2 g
initial temperature= 0°C = 273.15 K
final temperature= 234°C= 507.15
thermal capacity = 1 J/kg.M
latent heat of vaporization = 54 J/Kg
To find:
Entropy change ∆S = ?
Solution:
Entropy is measure of randomness of a system.
The change in entropy can be calculated in many ways depending upon the nature of substance & process like solid or liquid in isothermal process and when the process is not isothermal, gases are real or ideal etc.
If the process is isothermal (Temperature doesn't change) then the general equation to find change in entropy is,
[tex]\sf \Delta S = \frac{ q_{rev}}{T}= state \: function[/tex]
If the temperature of reaction is changing then change in entropy can be calculated by
[tex] \sf \: \Delta S = nC_p ln \frac{T_f}{T_i} [/tex]
Where n is number of moles of substance,
Cp is thermal capacity,
& T f and Ti are final and initial temperature respectively.
In the above reaction the water is being heated from 0°C (liquid) to 234°C (steam), the number of processes happening is
Entropy change (∆S1) for physical process where, water being heated from 0°C to 100°CEntropy change (∆S2) for phase transformation of isothermal process at 100°C where liquid H2O is turning into vapoursEntropy change (∆S3)for physical process, where vapours heated upto 234°CCalculating the number of moles of substance,
Given mass of water= 2g
Molecular mass of water = 18 g
[tex] \sf n = \frac{given \: mass \:}{molar \: mass} = \frac{2}{18} = 0.11moles[/tex]
Change in entropy for physical process 1,
The initial temperature of water is 0°C(273.15 K), and the water turns into vapour at 100°C (373.15 K), this is a purely heating of liquid at constant pressure, hence the formula that would be used is,
[tex]\sf \: \Delta S_1 = nC_p ln \frac{T_f}{T_i} \\ \sf \: \Delta S_1 = 0.11 \times 1 \times ln \frac{373.15}{273.15} \\ \sf \: \Delta S_1 = 0.11 \times ln 1.366 \\ \sf \: \Delta S_1 = 0.11 \times 0.311 \\ \sf \: \Delta S_1 = 0.0343 J/K[/tex]
At boiling point of water the change in entropy for phase transformation of liquid water to gaseous vapours at 100°C can be calculated,
Now the latent heat of vaporization (∆H) is given,
(Latent heat is the heat which is required to change the phase of any substance)
Substituting the data,
[tex]\sf \: \Delta S_2 = \frac{\Delta H}{T} \\ \sf \: \Delta S_2 = \frac{54}{373.15} \\ \sf \: \Delta S_2 = 0.145 J/K[/tex]
Now the third and final physical process of heating vapours from 100°C to 234°C, at constant pressure,
[tex] \sf \: \Delta S_3 = nC_p ln \frac{T_f}{T_i} \\ \sf \: \Delta S_3 = 0.11 \times 1 \times ln \frac{507.15}{373.15} \\ \sf \: \Delta S_3 = 0.11 \times ln 1.359 \\ \sf \: \Delta S_3 = 0.11 \times 0.306 \\ \sf \: \Delta S_3 = 0.0337J/K[/tex]
The total entropy change ∆S during the process is,
[tex] \sf \: \Delta S = \Delta S_1+ \Delta S_2 + \Delta S_3 \\ \sf \: \Delta S = 0.0343+ 0.145 + 0.0337 \\ \sf \: \Delta S = 0.219J/K[/tex]
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8. Il An 8.00 kg package in a mail-sorting room slides 2.00 m down a
chute that is inclined at 53.0° below the horizontal. The coefficient o
kinetic friction between the package and the chute's surface is 0.40.
Calculate the work done on the package by (a) friction, (b) gravity, and
(c) the normal force. (d) What is the net work done on the package?
Answer:
See below
Explanation:
Normal force = m g cos 53 = 8 kg * 9.8 m/s^2 * cos 53 = 47.1823 N
no work is done by this force
Force friction = coeff friction * force normal = .4 * 47.1823 = 7.55 N
work of friction = 7.55 * 2 m = 15.1 j
Force Downplane = mg sin 53 = 62.61 N
work = 62.61 * 2 = 125.22 j
Net Force downplane = force downplane - force friction = 55.06 N
net Work = force * distance = 55.06 N * 2 M = 110.12 j
Suppose a spacecraft of mass 17000 kg is accelerated to 0.14c. How much kinetic energy would it have? If you used the classical formula for kinetic energy, by what percentage would you be in error?
Answer:
1.32% error
Explanation:
You can derive the relativistic kinetic energy by integrating the velocity function over a differential change in momentum. Then use integration by parts to get the answer of:
[tex]KE=mc^2[gamma-1][/tex]
Gamma is the lorentz factor equal to:
[tex]gamma=\frac{1}{\sqrt{1-(v/c)^2}}[/tex]
Therefore the relativistic kinetic energy would be:
[tex]KE=mc^2[\frac{1}{\sqrt{1-(v/c)^2}}-1][/tex]
Plug everything in to get:
[tex]KE=(17000)(3x10^8)^2[\frac{1}{\sqrt{1-(0.14c/c)^2}}-1][/tex]
[tex]KE=(17000)(9x10^{16})[\frac{1}{\sqrt{1-0.0196}}-1][/tex]
[tex]KE=1.53x10^{21}[\frac{1}{\sqrt{1-0.0196}}-1][/tex]
[tex]KE=1.52x10^{19}J[/tex]
The classical non-relativistic formula for kinetic energy is:
[tex]KE=\frac{1}{2} mv^2[/tex]
Therefore the classical kinetic energy is:
[tex]KE=1.50x10^{19}J[/tex]
Use the error percentage formula, found online if you dont recall:
[tex]error=\frac{|KE_c-KE_r|}{KE_r} \frac{100}{1} =1.32[/tex]
five physical properties of metals
A 15-kg object accelerates at 3 m/s2. What is the net force acting on the object?
Answer:
Fnet = 45N
Explanation:
Fnet = m.a
= (15)(3)
= 45N