a water holding tank measures 115 m long, 45 m wide, and 9 m deep. traces of mercury have been found in the tank, with a concentration of 65 mg/l. what is the total mass of mercury in the tank? answer in units of kg

Answers

Answer 1

The tank that has a volume of 46575 m³ with a concentration of 65 mg/l has a total mass of mercury of: 3027.375 kg

To solve this problem the formulas and the procedures that we have to use are:

c= m(solute)/v(solution)v =  long * wide * deep

Where

c = concentration of solutionm = mass of solutev = volume of solution

Information about the problem:

long = 115 mwide = 45 mdeep = 9 m c= 65 mg/lv(solution)=?m(mercury)=?

Using the volume formula we get:

v=  long * wide * deep

v(solution) =  115 m * 45 m * 9 m

v(solution) = 46575 m³

By converting the volume units from m³ to liters we have:

v(solution) = 46575 m³ * 1000 l/1m³

v(solution) = 43.575*10^6 l

Applying the concentration formula and clearing the mass we get:

c= m(solute)/v(solution)

m(solute) = c * v(solution)

m(mercury) = 65 mg (mercury)/l (solution)  * 43.575*10^6 l (solution)

m(mercury) = 3.027375*10^9 mg

By converting the mass units from (mg) to (kg) we have:

m(mercury) = 3.027375*10^9 mg * 1 kg/ 1 * 10^6 mg

m(mercury) = 3027.375 kg

What is a solution?

In chemistry a solution is known as a homogeneous mixture of two or more components called:

SolventSolute

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A Water Holding Tank Measures 115 M Long, 45 M Wide, And 9 M Deep. Traces Of Mercury Have Been Found

Related Questions

A car increases its speed from 30 km/h to 60 km/h in 5 seconds. Its acceleration s (a) 1.66 m/s² (b) 5 km/h² (c) 16.6 km/h² (d) 5m/s² ​

Answers

Answer: 6 km/h²

Explanation:

Final Speed= 60 km/h

Initial Speed= 30 km/h

Time= 5 sec

Now,

60= 30 + Acceleration*5

⇒Acceleration = 6 km/h²

Pressure is a derived quantity with a formula suxh as Force per unit area what do you think which base quantities will be involved to form this derived quantity.​

Answers

Answer:

you can find answer in this

Explanation:

https://physics.nist.gov/cuu/Units/units.html

One pole of a magnet attracts a nail. Will the other pole of the magnet attract the nail? Explain. Also explain how a magnet sticks to a refrigerator door.

Answers

Yes, either pole generates a field that causes atoms within the iron to rotate in order to align their magnetic moments with the exterior field.

A magnet has a significant normal force acting on the door. The magnet is then held in place by frictional force.

What is a magnet?

A magnet is defined as a magnetic field-producing item capable of attracting unlike poles and repelling similar poles.

Magnets are manufactured from a class of metals known as ferromagnetic metals. These metals include nickel and iron. These metals are unusual in their ability to magnetize consistently. When we ask how a magnet works, we mean how the magnetic field of a magnet affects the thing.

There are many different sizes and shapes of magnets.

Magnets can be found in a variety of objects and settings, including toys, cabinet hardware, ornamental pieces placed on refrigerators, and other objects and sites.

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A ball is thrown up in the air and then caught 10 seconds later. How high did it go and what was the initial speed up? (6)

Answers

Answer:

high=125m

speed up=50m s-¹

Explanation:

consider acceleration due to gravity = 10m s-²

upward as positive

in t=5s

ball rest momentarily velocity=0

you can know this by drawing s-t graph

consider the upward movement t=0-5s

we now have v=0 t=5 a= -10 and need find u

so use a=[v-u]/t

-10=[0-u]/5

-50=-u

u=50 ms-¹

then let find the displacement

s = (v+u)t*1/2

s= 50*5*1/2

s=125m

Happens at the start of the game and after every touchdown. in flag football you may throw or punt the ball.

Answers

The correct answer is punt/kickoff

In gridiron football, a drive is started with a kickoff. The "kicking team" often kicks the ball to the "receiving team" of the opposite team during a kickoff. Until the player with the ball is tackled by the kicking team, goes out of bounds, scores a touchdown, or the play is otherwise deemed dead, the receiving team is then allowed to return the ball, i.e., attempt to move it towards the kicking team's end zone. Every half of play, the start of various overtime forms, and after scoring plays all feature kickoffs. At the beginning of each half, following a try, and following a successful field goal, the ball is sent into play through a kickoff.

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Complete question

Happens at the start of the game and after every touchdown. in flag football you may throw or punt the ball. options 1. Interception 2. Fumble

3. Punt/Kickoff  4. Down

who is Isacc.Newton??​

Answers

Answer:

Sir Isaac Newton contributed significantly to the field of science over his lifetime. He invented calculus (opens in new tab) and provided a clear understanding of optics. But his most significant work had to do with forces, and specifically with the development of a universal law of gravitation and his laws of motion

Explanation:

A genius with dark secrets. Isaac Newton changed the way we understand the Universe. Revered in his own lifetime, he discovered the laws of gravity and motion and invented calculus. He helped to shape our rational world view.

a total charge of 300 c flows past a given cross section of a conductor in 30 seconds. what is the value of the current?

Answers

Explanation:

Q = charge in C(coulombs)

I = current in A(amps)

t = time in s(seconds)

Q = I × t

I = Q / t

Substitute in given values.

I = 300C / 30s

= 10A

Hope this helped! ^^

The electric current generated by a charge of 300 coulombs passing through the cross section of a conductor in a time of 30 seconds is: 10 A

To solve this exercise the formula for electric current and the procedure we will use is:

I= q/t

Where:

I = intensity of the electric currentq= electric charget = time

Information about the problem:

q= 300 Ct = 30 sI=?1 C/s = 1 A

Applying the electric current intensity formula we have:

I= q/t

I= 300 C / 30 s

I= 10 A

What is electric current intensity?

In physics the intensity of the electric current is the magnitude that expresses the amount of electric charge or electric current in coulomb (c) that passes through an electrical conductor in a given time in seconds (s). Its unit of measurement in the international system is the Ampere (A).

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a rocket was launched into the air from a podium 6 feet off the ground. the rocket path is represented by the equation h(t)

Answers

The average rate of change of height from the initial launch to the maximum height is 180 feet.

The given function is

[tex]h(t) = -16t^{2} +120t+6[/tex]

The average rate of change of h(t) from t=a to t=b is given by:

[tex]\frac{h(b)-h(a)}{b-a}[/tex]

Vertical Velocity will be zero at maximum height. To find maximum height we differentiate the equation to get an equation for the velocity and set it to zero.

On differentiating we get,

h'(t) = -16(2)t + 120

h'(t) = -32t + 120

now equating to zero we get

t = 3.75 s

This is the time at which the rocket reaches maximum height.

The initial launch occurs at t = 0

substituting it in the original equation we get

[tex]h(t)[/tex] = [tex]-16(0)^{2}+120(0)+6[/tex]

[tex]h(t) = 6[/tex]

The average rate of change from the initial launch to the maximum height is:

[tex]\frac{h(3.75)-h(0)}{3.75-0}[/tex]

= [tex]\frac{681-6}{3.75}[/tex]

= 180

Hence the average rate of change from the initial launch to the maximum height is 180 feet.

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An amusement park designer wants his swing to have a centripetal
acceleration of 21 m/s2. If the velocity of the swing is 13 m/s, how long
should the chain on the swing be?

Answers

The chain on the swing should be 8.0 m long .

Centripetal Acceleration ( a ) = v ² / r ........... Eq. 1

It is given that ,

a = 21 m / s ²

v = 13 m / s

Now ,  using the values of ' a ' and ' v ' i.e. 21 m / s ² & 13 m / s respectively in Eq. 1

a =  v ² / r

21 = ( 13 ) ² / r

21 = ( 13 x 13 ) / r

r = ( 13 x 13 ) / 21

r = 8.047 m

⇒ r = 8.0 m ( rounded off to nearest tenth )

Hence , the chain on the swing should be 8.0 m long .

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A 100kg box is on an incline of 60 degrees. What is the perpendicular force

Answers

Answer:

490N

Explanation:

the formula to use for perpendicular force is:

[tex]Fg=mg(cos\theta)[/tex]  

now we plug in:

*for g, it can be 9.8 m/s^2 or 10 m/s^2 depending on your teacher

[tex]Fg=(100)(9.8)(cos60)[/tex]

then you get:

[tex]Fg=490N[/tex]

Help please ;((((((((

Answers

Answer:

42- electromagnetic force

Explanation:

electrons keep orbiting around the nucleus thanks to electromagnetic force :)

hope this helped!

Review. For a certain type of steel, stress is always proportional to strain with Young's modulus 20 × 10¹⁰ N/m² . The steel has density 7.86× 10³kg / m³. It will fail by bending permanently if subjected to compressive stress greater than its yield strength бy = 400MPa. A .rod 80.0cm long, made
of this steel, is fired at 12.0 m/s straight at a very hard wall.(b) After the front end of the rod hits the wall and stops, the back end of the rod keeps moving as described by Newton's first law until it is stopped by excess pressure in a sound wave moving back through the rod. What time interval elapses before the back end of the rod receives the message that it should stop?

Answers

[tex]1.58\times 10^{-4}\ \mathrm{s}$[/tex] is the time interval elapses before the back end of the rod receives the message that it should stop.

Given:

Length of the rod, L = 80 cm = 0.800 m

Young's modulus, Y = [tex]20 \times 10^{10}\;N/m^{2}[/tex]

steel density, [tex]\rho = 7.86 \times 10^{3}\;kg/m^{3}[/tex]

The speed of the wave in the rod is,

[tex]$v = \sqrt{\frac{Y}{\rho}} = \sqrt{\frac{20\times 10^{10}\ \mathrm{N/m^2}}{7.86\times 10^3\ \mathrm{kg/m^3}}} = 5044\ \mathrm{m/s}$[/tex]

Consequently, the length of the rod's end is traveled by the wave in at

[tex]$t=\frac{L}{v} = \frac{0.800\ \mathrm{m}}{5044\ \mathrm{m/s}} = 1.58\times 10^{-4}\ \mathrm{s}$[/tex]

Hence, [tex]1.58\times 10^{-4}\ \mathrm{s}$[/tex] is the time interval elapses before the back end of the rod receives the message that it should stop.

What are Newtons Laws?

The three fundamental laws of classical mechanics known as Newton's laws of motion describe how an object's motion and the forces acting on it interact. The following paraphrase of these statutes is available

Unless a force acts upon a body, it remains at rest or in continual straight-line motion.

When a force acts on a body, the force is equal to the time rate at which the body's momentum changes.

When two bodies exert force on one another, the direction and amount of the force are opposed.

Isaac Newton first identified the three laws of motion in his 1687 book Philosophize Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy).

They served as the cornerstone for classical mechanics as Newton used them to examine and explain the motion of numerous physical objects and systems. The conceptual foundations of classical physics have been reconstructed in several ways since Newton, utilizing various mathematical techniques that have revealed insights that were hidden in the original, Newtonian formulation.

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Plasma is one of the fundamental states of matter and consists of a:
A) liquid at high temperature
B) totally or partially ionized gas, electrically neutral
C) partially ionized gas, with electric charge
D) partially ionized liquid
E) partially ionized liquid, electrically neutral

Answers

Answer:

a

Explanation:

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if you run off the pavement, you should: steer straight ahead and speed up steer straight and slow down before attempting to return to the pavement turn the steering wheel quickly toward the road apply the brakes hard submit answer

Answers

If you run off the pavement, you should turn the steering wheel quickly toward the road and is denoted as option C.

What is Pavement?

This is a path which is found in almost all roads and is designed to enhance foot traffic in most climes. This is the path where individuals walk so as not to get hit down by a vehicle.

In a situation where a car runs into the pavement, the best choice is to turn the steering wheel quickly toward the road as braking hard could damage the brakes of the car and cause accident in subsequent trips.

This is therefore why option C was chosen as the correct choice.

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Answer: Steer straight and slow down before attempting

Explanation:

three scientists measure the standard meter bar kept at the international bureau of standards (the definition of a meter). their measurements are 1.01 m, 0.99 m, and 1.00 m. are their measurements accurate, precise, or both? group of answer choices accurate but not precise neither accurate nor precise precise by not accurate accurate and precise

Answers

The measurements by the different scientists were 1.01 m, 0.99 m and 1.00 m,  which are not exactly same as the standard value of a meter. But all the three values are very much close to each other.

Meter is a fundamental unit of length in the metric system and in the International Systems of Units (SI). It is denoted by m.

Therefore the measurements for the bar kept at the international bureau of standards taken by the three scientists were precise but not accurate.

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Which question would best determine how electromagnetic and mechanical waves are similar?

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The question 'How do electromagnetic and mechanical waves compare?'

There are many similarities between electromagnetic waves and mechanical waves.

In Physics, both electromagnetic and mechanical waves have amplitude, wavelength, and frequency.

Electromagnetic waves can travel through empty spaces as well such as vacuums, gases, liquids, and solids.

While mechanical waves can not propagate through space they can only travel through liquids, solids, and gases.

water waves and ripples in a pool are examples of mechanical waves.

Examples of EM waves are radio signals and light waves, microwaves, and X-rays.

To put it simply, EM waves do not require a medium to travel whereas mechanical waves require a medium to propagate.

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which truth did isaac newton’s investigations of gravity explain? jupiter has more moons than earth. jupiter has more moons than earth. the sun is more massive than earth. the sun is more massive than earth. gravity acts on all objects in the universe. gravity acts on all objects in the universe. earth is not the center of the universe. earth is not the center of the universe.

Answers

Newton's investigations of gravity explain the truth that Jupiter has more moons than Earth.

The fact that Jupiter has more moons than Earth was first discovered by Galileo Galilei in 1610, and it was later confirmed by Newton. In addition to having more moons, it is also thought that Jupiter may be home to some of the most powerful magnetic fields in the solar system.

What was explained by Isaac Newton's law of gravity?

Every particle in the cosmos attracts every other particle with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers, according to Newton's law of universal gravitation.

Thus, the equation for universal gravity has the following structure:

[tex]{\displaystyle F=G{\frac {m_{1}m_{2}}{r^{2}}}}{\displaystyle[/tex]

where r is the distance between the centers of the two objects' masses, m1 and m2 are their respective masses, G is the gravitational constant, and F is the gravitational force acting between them.

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The correct answer is; Gravity acts on all objects in the universe.

The answer above is incorrect…

13. Two identical metallic spheres A and B, each carry- ing a charge q, repel each other with a force F. A third metallic sphere C of the same size, but un- charged, is successively made to touch the spheres A and B, and then removed away. What is the force of repulsion between A and B? (Ans. 3F/8) 4.​

Answers

Answer:

Who knows the answer please I need the answer

Which two types of potential energies would be types of mechanical energies?

electrical and kinetic
nuclear and chemical
radiant and thermal
elastic and gravitational

Answers

The two types of potential energies which would be types of mechanical energies are elastic and gravitational.

The correct answer choice is option D

What is meant by potential energy?

Potential energy means the energy a body possess in relation to its position. Other forms of energy include

Electrical energyKinetic energyChemical energySound energyNuclear energy Thermal energy Radiant energy

Kinetic energy is the energy a body possesses due to its motion.

So therefore, the two types of potential energies which would be types of mechanical energies are elastic and gravitational. The correct answer choice is option D

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Answer: it is d

Explanation: i took the unit test on edge

Q|C The speed of a one-dimensional compressional wave traveling along a thin copper rod is 3.56 km/s . The rod is given a sharp hammer blow at one end. A listener at the far end of the rod hears the sound twice, transmitted through the metal and through air, with a time interval Δt between the two pulses.(d) Imagine that the copper rod is replaced by another material through which the speed of sound is v_r . What is the length of the rod in terms of t and v_r ?

Answers

The length of rod in terms v(r) and t is L = [  Δt / (1/343) - (1/v(r)) ].

3.56 km/s is the speed of a one-dimensional compressional wave moving along a thin copper rod.

At one end of the rod, a hard hammer strike is delivered. With a time interval of Δt between the two pulses, a listener at the other end of the rod hears the sound twice as it travels through the metal and the air.

The time interval is given by t = L/v.

We know, The speed of air, v(air) = 343 m/s

Now,

When the copper rod is swapped out for a different substance and the sound speed is measured as v(r).

The delay between pulses arrivals is:

Δt = L [(1/v(air)) - (1/v(copper))]

Then,

L = [  Δt / (1/v(air)) - (1/v(r)) ]

L = [  Δt / (1/343) - (1/v(r)) ]

Here L is the length of the rod, Δt is in seconds and v(r) is the speed of sound in the rod.

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The furniture was designed to go a top speed of 87.0mph. How far would this sofa travel to the mall 1.00 hour away?

Answers

The sofa with a top speed of 87 mph would travel a distance of 43.5 miles to the mall 1 hour away.

Considering the sofa accelerates constantly throughout the motion,

s = ( u + v )  t / 2

s = Distance

u = Initial velocity

v = Final velocity

t = Time

v = 87 mph

t = 1 hr

u = 0

s = ( u + v )  t / 2

s = ( 0 + 87 ) 1 / 2

s = 43.5 mi

This is an equation of motion.

Therefore, the sofa would travel a distance of 43.5 miles

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Answer please with working out

Answers

1.
a. Speed = distance/time
b. 1500/300 = 5m/s
c. 10 - 2 = 8/2.4 = 3.33 seconds

2.
a. 0.46 x 2.4 = 1.104 metres
b. 78.4/8 = 9.8 m/2²

Answer:

(1) a) S=D/T

b)5m/s

c)3.33s

(2) a) 1.104m

Explanation:

(1) b) S=D/T

 S=1500/300

 S=5m/s

c) T= V-U/a

 v=10

 u= 2

 a= 2.4

10-2=8/2.4=3.33s

(2) a) d=s×t

 0.46×2.4=1.104m



10 pts the classic millikan oil drop experiment was the first to obtain an accurate measurement of the charge on an electron. in it, oil drops were suspended against the gravitational force by a vertical electric field. consider an oil drop with a weight of 1.2 x 10-14n, if the drop has a single excess electron, find the magnitude (in n/c) of the electric field needed to balance its weight. your should round your answer to an integer, indicate only the number, do not include the unit.

Answers

the magnitude of the electric field needed to balance its weight is  

0.75 ×10⁵N/C

The oil drop method was performed by Robert A Millikan in 1909.

It is used to determine the size of the charge  on an atom.

Millikan used vacuum pump oil for this his experiment.

to find out the magnitude of electric field

W = q E,

W = weight (W = mg)

q = charge (1.6×10⁻¹⁴C)

E = Electric field

→ oil drops were suspended against the gravitational force by a vertical electric field such that its weight is balanced by the electron force i.e.

W =  1.2× 10⁻¹⁴

1.2× 10⁻¹⁴ = q × E

E =  1.2× 10⁻¹⁴N/ 1.6×10⁻¹⁹C

E =  0.75 ×10⁵N/C

the magnitude of the electric field needed to balance its weight is  

0.75 ×10⁵N/C

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A wire 2.80m in length carries a current of 5.00A in a region where a uniform magnetic field has a magnitude of 0.390T. Calculate the magnitude of the magnetic force on the wire assuming the angle between the magnetic field and the current is (b) 90.0° .

Answers

The force on the wire will be

F = 5.46 Newton.

We have a current carrying wire in a uniform magnetic field.

We have to determine the magnitude of the magnetic force on the wire assuming the angle between the magnetic field and the current is 60.0°.

What is the magnitude of force acting on a current (I) carrying wire of length (L) placed in a Magnetic field (B)?

The force on the current carrying wire will be -

F = IBL sinθ

According to the question, we have -

L = 2.80 m

I = 5 A

B = 0.39 T

Therefore -

F = IBL sinθ

F = 5 x 0.39 x 2.80 x sin(90)

F = 5.46 x sin(90)

F = 5.46 Newton

Hence, the force on the wire will be

F = 5.46 Newton

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The magnitude of the magnetic force on the wire 5.46 N.

To find the magnetic force, the values given are:

Length A = 2.80m

Current I = 5 A

Magnetic field B = 0.390 T

Angle = 90° .

What is meant by magnetic force?

The attraction or repulsion that arises between electrically charged particles because of their motion is called Magnetic force.Magnetic force is the basic force which is responsible for such effects as the action of electric motors and the attraction of magnets.A force experienced through the magnetic field with some moving charges is perpendicular to its own velocity.The formula to find the magnetic force,

                      F =iBLsinθ Newton

Substituting the values given,

Magnetic force,

F = 5 A × 0.390 T × 2.80 m × Sin 90°

  = 5 A × 0.390 T × 2.80 m × 1

F = 5.46 N.

The magnitude of the magnetic force on the wire 5.46 N.

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Positively charged particles of radiation emitted from the decay of radioactive substances are known as.

Answers

Positively charged particles of radiation emitted from the decay of radioactive substances are known as alpha particles.

What is an alpha particle?

A helium nucleus that some radioactive compounds release that was once thought to be a ray. Ionized alpha particles are made up of two protons, neutrons ( no charge), and no electrons.

Two protons and two neutrons from the atom's nucleus combine to form the positive charge alpha particles (α). The most toxic radioactive materials, such as uranium, radium, and polonium, decay to produce alpha particles.

A ray-like emission of a helium nucleus from some radioactive materials.

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an object of mass m is traveling at constant speed v in a circular path of radius r. how much work is done by the centripetal force on mass m during an angular displacement of 2π revolutions?: *

Answers

The work done is by the centripetal force on mass m during an angular displacement of 2π revolutions mv²2π /r J

Centripetal force - a force acts on an moving object in circular path.

the centripetal force is given by

F= mv²/r       (equation1)

Work done is given by

W = Fd          (equation 2)

d = 2π

work is done by the centripetal force on mass m during an angular displacement of 2π revolutions is given by:

to calculate work done using equation 1 in 2  we get

W = mv² d/r

 W = mv² × 2π /r J

The work done is by the centripetal force on mass m during an angular displacement of 2π revolutions mv²2π /r J

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A tank for compressed gas has a maximum safe pressure limit of 850 kPa. The pressure
gauge reads 425 kPa when the temperature is 28°C. What is the highest temp in degrees
Celsius the tank can withstand safely?

Answers

Answer: 56 degrees Celsius

Explanation: 425 is half of 850, so we double the temp to get the answer.

A karate expert executes a swift blow and breaks a cement block with her bare hand. The magnitude of the force on her hand is.

Answers

3.141592653589793238

Explanation:

3.141592653589793238

The power output of a certain public-address speaker is 6.00W . Suppose it broadcasts equally in all directions.(b) At what distance from the speaker would the sound be barely audible?

Answers

The distance from the speaker would the sound be barely audible is 477.46km.

What is distance?

It's how far away two objects or locations are measured numerically as distance. Distance in physics or common language can refer to a physical length or an assumption based on other factors (e.g. "two counties over"). Sometimes the symbol |AB| is used to indicate how far apart two points are. "Distance from A to B" and "Distance from B to A" are typically equivalent terms. A distance function or metric in mathematics is an extension of the idea of physical distance; it defines what it means for components in a space to be "near to" or "far away" from one another. Distance is a non-numerical unit of measurement in the social sciences and psychology.

Explanation:

Sound audible(barely) = 0dB

I= 10.709*I/[tex]10^{-10}[/tex]=0

I= [tex]10^{-12}[/tex]*[tex]10^{0}[/tex]=[tex]10^{-12}[/tex]w/[tex]m^{2}[/tex]

[tex]distance(r)=\sqrt[]{\frac{P}{4\pi I} } =\sqrt[]{\frac{6}{4\pi * 10^{-12} } } =477.46 km[/tex]

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Rank the wavelengths of the following quantum particles from the largest to the smallest. If any have equal wavelengths, display the equality in your ranking. (a) a photon with energy 3eV(b) an electron with kinetic energy 3eV(c) a proton with kinetic energy 3eV(d) a photon with energy 0.3eV(e) an electron with momentum 3eV/c

Answers

The wavelengths of the following quantum particles from the largest to the smallest is (d) > (a) = (e) > (b) > (c)

De Broglie proposed that because light has both wave and particle properties, matter exhibits both wave and particle properties. This property has been explained as the dual behavior of matter. From his observations, de Broglie derived the relationship between the wavelength and momentum of matter. This relationship is known as de Broglie's relationship.

De Broglie's relationship is given by  [tex]\lambda=\frac{h}{mv}[/tex] .

This can be written as [tex]\lambda=\frac{h}{p}[/tex]  .....(1) where λ  is known as de Broglie wavelength and p is momentum , h = Plank’s constant .

As we know that mass of proton is greater than electron and photon .

(a)For photon , the momentum is given by [tex]p=\frac{E}{c}[/tex]     ...(2)  where c is the speed is the speed of light .

Putting E = 3eV in equation (2) , we get

              [tex]p=\frac{3\times 1.6\times10^-^1^9}{3\times 10^8} \\p=1.6\times10^-^2^7Js/m[/tex]

Putting this value of p in equation (1) , we get

  [tex]\lambda=\frac{6.62\times10^{-34}}{1.6\times10^{-27}}\\\lambda=4.13\times10^{-7}[/tex]

(b) As we know that  kinetic energy is given by

         [tex]K.E=\frac{1}{2} mv^2\\\\2K.E = mv^2\\2K.E\times m = m^2v^2\\2K.E\times m = (mv)^2\\2K.E\times m = p^2\\\\\sqrt{2K.E\times m }=p[/tex]      ...(3)

Where mass of electron is [tex]9.1\times10^-^3^1 kg[/tex] .

Putting K.E = 3eV in equation (3) , we get

    [tex]\sqrt{2K.E\times m }=p\\p=\sqrt{2\times3\times1.6\times10^{-19} \times 9.31\times10^{-31} }\\p=\sqrt{89.376\times10^{-50}} \\p=9.45\times10^{-25}Js/m[/tex]

Putting this value of p in equation (1) , we get

[tex]\lambda=\frac{6.62\times10^{-34}}{9.45\times10^{-25}}\\\lambda=0.7005\times10^{-9}[/tex]

(c) Putting [tex]m=1.67\times10^{-27}kg[/tex] and K.E = 3eV in equation (3) , we get

     [tex]\sqrt{2K.E\times m }=p\\p=\sqrt{2\times3\times1.6\times10^{-19} \times 1.67\times10^{-27} }\\p=\sqrt{16.032\times10^{-46}} \\p=4.003\times10^{-23}Js/m[/tex]

Putting this value of p in equation (1) , we get

[tex]\lambda=\frac{6.62\times10^{-34}}{4.003\times10^{-23}}\\\lambda=1.65\times10^{-11}[/tex]

(d) Putting E = 0.3eV in equation (2) , we get

   [tex]p=\frac{0.3\times 1.6\times10^-^1^9}{3\times 10^8} \\p=1.6\times10^-^2^8Js/m[/tex]

Putting this value of p in equation (1) , we get

[tex]\lambda=\frac{6.62\times10^{-34}}{1.6\times10^{-28}}\\\lambda=4.13\times10^{-6}[/tex]

(e) Putting [tex]p=3eV/c[/tex] in equation (1) , we get

    [tex]\lambda=\frac{6.62\times10^{-34}\\\times3\times10^8}{3\times1.6\times10^{-19}}\\\lambda=4.13\times10^{-7}[/tex]

On comparing the wavelength order should be (d) > (a) = (e) > (b) > (c) .

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