College Physics

atomic spectra:

binding energy:

blackbody radiation:

blackbody:

bremsstrahlung:

Compton effect:

characteristic x rays:

correspondence principle:

de Broglie wavelength:

gamma ray:

Heisenberg’s uncertainty principle:

infrared radiation:

ionizing radiation:

microwaves:

(29.52)

p=h

λ

.

Entering the known value for Planck’s constanthand given the wavelengthλ, we obtain

(29.53)

p = 6.63×^10

− 34

J⋅ s

550 × 10 –9m

= 1. 21 × 10

− 27

kg ⋅ 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 (Fnet= 0). (29.54)

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, (29.55)

where p 1 is the photon momentum before the collision andp′ 2 is the dust momentum after the collision. The mass and recoil velocity of the

dust aremandv, respectively. Solving this forv, the requested quantity, yields

v=p (29.56)

m,

where pis the photon momentum found in part (a). Entering known values (noting that a microgram is 10

−9

kg) gives

(29.57)

v =

1.21× 10 −27kg ⋅ m/s

1.00× 10 – 9kg

= 1.21× 10 –18m/s.

Discussion

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.

Glossary

the electromagnetic emission from atoms and molecules

also called thework function; the amount of energy necessary to eject an electron from a material

the electromagnetic radiation from a blackbody

an ideal radiator, which can radiate equally well at all wavelengths

German forbraking radiation; produced when electrons are decelerated

the phenomenon whereby x rays scattered from materials have decreased energy

x rays whose energy depends on the material they were produced in

in the classical limit (large, slow-moving objects), quantum mechanics becomes the same as classical physics

the wavelength possessed by a particle of matter, calculated byλ=h/p

alsoγ-ray; highest-energy photon in the EM spectrum

a fundamental limit to the precision with which pairs of quantities (momentum and position, and energy and

time) can be measured

photons with energies slightly less than red light

radiation that ionizes materials that absorb it

photons with wavelengths on the order of a micron (μm)

CHAPTER 29 | INTRODUCTION TO QUANTUM PHYSICS 1055