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Problem-solving strategy

  1. Identify which physical principles are involved.
  2. Solve the problem using strategies outlined in the text.

[link] illustrates how these strategies are applied to an integrated-concept problem.

Recoil of a dust particle after absorbing a photon

The following topics are involved in this integrated concepts worked example:

Photons (quantum mechanics)
Linear Momentum

A 550-nm photon (visible light) is absorbed by a 1 . 00-μg size 12{1 "." "00-μg"} {} particle of dust in outer space. (a) Find the momentum of such a photon. (b) What is the recoil velocity of the particle of dust, assuming it is initially at rest?

Strategy Step 1

To solve an integrated-concept problem , such as those following this example, we must first identify the physical principles involved and identify the chapters in which they are found. Part (a) of this example asks for the momentum of a photon , a topic of the present chapter. Part (b) considers recoil following a collision , a topic of Linear Momentum and Collisions .

Strategy Step 2

The following solutions to each part of the example illustrate how specific problem-solving strategies are applied. These involve identifying knowns and unknowns, checking to see if the answer is reasonable, and so on.

Solution for (a)

The momentum of a photon is related to its wavelength by the equation:

p = h λ . size 12{p= { {h} over {λ} } } {}

Entering the known value for Planck’s constant h size 12{h} {} and given the wavelength λ size 12{λ} {} , we obtain

p = 6.63 × 10 34 J s 550 × 10 –9 m = 1 . 21 × 10 27 kg m/s . alignl { stack { size 12{p= { {6 "." "63"´"10" rSup { size 8{-"34"} } " J" cdot s} over {5 "." "50"´"10" rSup { size 8{ +- 9} } " m"} } } {} #=1 "." "21"´"10" rSup { size 8{-"27"} } " kg" cdot "m/s" "." {} } } {}

Discussion for (a)

This momentum is small, as expected from discussions in the text and the fact that photons of visible light carry small amounts of energy and momentum compared with those carried by macroscopic objects.

Solution for (b)

Conservation of momentum in the absorption of this photon by a grain of dust can be analyzed using the equation:

p 1 + p 2 = p 1 + p 2 ( F net = 0 ) . size 12{p rSub { size 8{1} } +p rSub { size 8{2} } =p rSub { size 8{1} } '+p rSub { size 8{2} } '" " \( F rSub { size 8{"net"} } =0 \) } {}

The net external force is zero, since the dust is in outer space. Let 1 represent the photon and 2 the dust particle. Before the collision, the dust is at rest (relative to some observer); after the collision, there is no photon (it is absorbed). So conservation of momentum can be written

p 1 = p 2 = mv , size 12{p rSub { size 8{1} } =p rSub { size 8{2} } ' = ital "mv"} {}

where p 1 size 12{p rSub { size 8{1} } } {} is the photon momentum before the collision and p 2 size 12{p rSub { size 8{2} } ' } {} is the dust momentum after the collision. The mass and recoil velocity of the dust are m size 12{m} {} and v size 12{v} {} , respectively. Solving this for v size 12{v} {} , the requested quantity, yields

v = p m , size 12{v= { {p} over {m} } } {}

where p size 12{p} {} is the photon momentum found in part (a). Entering known values (noting that a microgram is 10 9 kg size 12{"10" rSup { size 8{ - 9} } " kg"} {} ) gives

v = 1 . 21 × 10 27 kg m/s 1 . 00 × 10 9 kg = 1 . 21 × 10 –18 m/s. alignl { stack { size 12{v= { {1 "." "21"´"10" rSup { size 8{-"27"} } " kg" cdot "m/s"} over {1 "." "00"´"10" rSup { size 8{ +- 9} } " kg"} } } {} #=1 "." "21"´"10" rSup { size 8{-"18"} } " m/s" "." {} } } {}


The recoil velocity of the particle of dust is extremely small. As we have noted, however, there are immense numbers of photons in sunlight and other macroscopic sources. In time, collisions and absorption of many photons could cause a significant recoil of the dust, as observed in comet tails.

Section summary

  • The particle-wave duality refers to the fact that all particles—those with mass and those without mass—have wave characteristics.
  • This is a further connection between mass and energy.

Conceptual questions

In what ways are matter and energy related that were not known before the development of relativity and quantum mechanics?

Got questions? Get instant answers now!

Questions & Answers

what is fluid
Anthony Reply
anything that flows is Liquid.
How submarines floats one water the same time sink in water
Courage Reply
A submarine has the ability to float and sink. The ability to control buoyancy comes from the submarine'strim or ballast tanks which can be filled with either water or air, depending on whether the submarine needs to floator sink. When the submarine floats it means its trim tanks are filled with air
what is work
Ojo Reply
Force times distance
product of force and distance...
Is physics a natural science?
Adebisi Reply
what is the difference between a jet engine and a rocket engine.
Samuel Reply
explain the relationship between momentum and force
Joseph Reply
A moment is equivalent multiplied by the length passing through the point of reaction and that is perpendicular to the force
How to find Squirrel frontal area from it's surface area?
Pooja Reply
how do we arrange the electronic configuration of elements
Muhammed Reply
hi guys i am an elementary student
benedict Reply
are you an elementary student too?
no bro
what is the four equation of motion
what is strain?
Change in dimension per unit dimension is called strain. Ex - Change in length per unit length l/L.
strain is the ratio of extension to length..=e/l...it has no unit because both are in meters and they cancel each other
How is it possible for one to drink a cold drink from a straw?
Karanja Reply
most possible as it is for you to drink your wine from your straw
state the law of conservation of energy
Sushma Reply
energy can neither be destroy or created,but can be change from one form to another
it can neither be created nor destroyed
its so sample question dude
what is the difference between a principle and a law?
Mary Reply
where are from you wendy .?
you are beautiful
are you physics student
laws are ment to be broken
hehe ghulam where r u from?
principle are meant to be followed
south Africa
here Nigeria
principle is a rule or law of nature, or the basic idea on how the laws of nature are applied.
Rules are meant to be broken while principals to be followed
principle is a rule or law of nature, or the basic idea on how the laws of nature are applied.
what is momentum?
prakash Reply
is the mass times velocity of an object
it is the product of mass and velocity of an object.
The momentum possessed by a body is generally defined as the product of its mass and velocity m×v
momentum is the product of the mass of a body of its velocity
what about kg it is changing or not
vijay Reply
no mass is the quantity or amount of body so it remains constant everywhere
remains constant
mass of an object is always constant. and that is universally applied.
mass of a body never changes but the weight can change due to variance of gravity at different points of the world
what is hookes law
mass of an object does not change
Is weight a scalar quantity
esther Reply
weight is actually a force of gravity with which earth attracts us downwards so it is a vector quantity. and it has both direction and magnitude
weight is the earth pull of the body
why does weight change but not mass?
Theo, the mass of an object can change but it depends on how you define that object. First, you need to know that mass is the amount of matter an object has, and weight is mass*gravity (the "force" that attracts object A to the object B mass).
So if you face object A with object B, you will get a different result than facing object A with object C, so the weight of object A changes but not its mass.
Now, if you have an object and you take a part away from it, you are changing it mass. Lets use the human body and fat loss process as an example.
When you lose weight by doing exercise, you are being attracted by the same object before and after losing weight so the change of weight is related to a change of mass not a change of gravity.
The explanation of this is simple, we are composed of smaller particles, which are itself objects, so the loose of mass of an object actually is the separation of one object is two different ones.
But if you define an object because of its form and characteristics and not the amount of mass, then the object is the same but you have taken a part of it mass away.
Theo, weight =mass. gravity, here mass is fixed everywhere but gravity change in different places so weight change not mass.
yup weight changes and mass does not. That's why we're 1/3 our weight on the moon
weight is the product of mass × velocity w=m×v = m(v-u) but v=u+1/2at^ weight is a scalar quantity mass of an obj is the amount of particles that obj cont
mass is fixed always while weight is dynamic
Why does water wet glass but mercury does not?
thanks guys
Yusuf Shuaibu, for water the Adhessive force between water molecules and glass is greater than the cohessive force between it's own molecules but for Mercury the cohessive force will be greater in comparison with adhessive force. For this water wet glass but Mercury does not.

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Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
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