bei48482_FM

Example 2.7

The linear attenuation coefficient for 2.0-MeV gamma rays in water is 4.9 m^1. (a) Find the rel-

ative intensity of a beam of 2.0-MeV gamma rays after it has passed through 10 cm of water.

(b) How far must such a beam travel in water before its intensity is reduced to 1 percent of its

original value?

Solution

(a) Here x(4.9 m^1 )(0.10 m)0.49 and so, from Eq. (2.25)

exe0.490.61

The intensity of the beam is reduced to 61 percent of its original value after passing through

10 cm of water.

(b) Since I 0 I100, Eq. (2.26) yields

x0.94 m

2.9 PHOTONS AND GRAVITY

Although they lack rest mass, photons behave as though they have

gravitational mass

In Sec. 1.10 we learned that light is affected by gravity by virtue of the curvature of

spacetime around a mass. Another way to approach the gravitational behavior of light

follows from the observation that, although a photon has no rest mass, it nevertheless

interacts with electrons as though it has the inertial mass

m (2.27)

(We recall that, for a photon, phcand c.) According to the principle of equiv-

alence, gravitational mass is always equal to inertial mass, so a photon of frequency 

ought to act gravitationally like a particle of mass hc^2.

The gravitational behavior of light can be demonstrated in the laboratory. When we

drop a stone of mass mfrom a height Hnear the earth’s surface, the gravitational pull of

the earth accelerates it as it falls and the stone gains the energy mgHon the way to the

ground. The stone’s final kinetic energy^12 m^2 is equal to mgH, so its final speed is ^2 gH.

All photons travel with the speed of light and so cannot go any faster. However, a

photon that falls through a height Hcan manifest the increase of mgHin its energy by

an increase in frequency from to (Fig. 2.30). Because the frequency change is

extremely small in a laboratory-scale experiment, we can neglect the corresponding

change in the photon’s “mass” hc^2.

h



c^2

p





Photon “mass”

ln 100



4.9 m^1

ln(I 0 I)





I



I 0

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