<< Chapter < Page Chapter >> Page >

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 the difference between a principle and a law
the law is universally proved. The principal depends on certain conditions.
state Faraday first law
aliyu Reply
it states that mass of an element deposited during electrolysis is directly proportional to the quantity of electricity discharge
what does the speedometer of a car measure ?
Jyoti Reply
Car speedometer measures the rate of change of distance per unit time.
describe how a Michelson interferometer can be used to measure the index of refraction of a gas (including air)
using the law of reflection explain how powder takes the shine off a person's nose. what is the name of the optical effect?
is higher resolution of microscope using red or blue light?.explain
what is dimensional consistent
In engineering and science, dimensional analysis is the analysis of the relationships between different physical quantities by identifying their base quantities and units of measure and tracking these dimensions as calculations or comparisons are performed
can sound wave in air be polarized?
Unlike transverse waves such as electromagnetic waves, longitudinal waves such as sound waves cannot be polarized. ... Since sound waves vibrate along their direction of propagation, they cannot be polarized
A proton moves at 7.50×107m/s perpendicular to a magnetic field. The field causes the proton to travel in a circular path of radius 0.800 m. What is the field strength?
Celedonio Reply
derived dimenionsal formula
Ajak Reply
what is the difference between mass and weight
Isru Reply
assume that a boy was born when his father was eighteen years.if the boy is thirteen years old now, how is his father in
what is head-on collision
Javaid Reply
what is airflow
Godswill Reply
derivative of first differential equation
Haruna Reply
why static friction is greater than Kinetic friction
Ali Reply
draw magnetic field pattern for two wire carrying current in the same direction
Ven Reply
An American traveler in New Zealand carries a transformer to convert New Zealand’s standard 240 V to 120 V so that she can use some small appliances on her trip.
nkombo Reply
What is the ratio of turns in the primary and secondary coils of her transformer?
what is energy
How electric lines and equipotential surface are mutually perpendicular?
Abid Reply
The potential difference between any two points on the surface is zero that implies È.Ŕ=0, Where R is the distance between two different points &E= Electric field intensity. From which we have cos þ =0, where þ is the angle between the directions of field and distance line, as E andR are zero. Thus
sorry..E and R are non zero...

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play

Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'College physics' conversation and receive update notifications?