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Chapter 38: Q36P (page 1183)

Gamma rays of photon energy 0.511 MeV are directed vonto an aluminium target and are scattered in various directions by loosely bound electrons there.

(a) What is the wavelength of the incident gamma rays?

(b) What is the wavelength of gamma rays scattered at 90鈭�to the incident beam?

(c) What is the photon energy of the rays scattered in this direction?

Short Answer

Expert verified

(a) The wavelength of the incident gamma rays is2.43鈥塸尘

(b) The wavelength of the gamma rays scattered at 90 degrees to the incident beam is 4.86鈥塸尘.

(c) The photon energy for the ray scattered in the direction is 0.255鈥塎别痴.

Step by step solution

01

The wavelength of the incident gamma rays.

(a)

Use the value of hc=1240鈥塭痴鈰�nmthen it gives;

位=hcE=1240鈥塶尘鈰�eV(0.511鈥塎别痴)=2.43脳10鈭�3nm=2.43鈥塸尘

Hence, the wavelength of the incident gamma rays is2.43鈥塸尘 .

02

The wavelength of the gamma rays scattered at 90∘ to the incident beam.

(b)

The wavelength of the gamma rays is calculated as follows:

位'=位+螖位=位+hmc(1鈭�cos蠒)=2.43+(2.34)(1鈭�cos90鈭�)=4.86鈥塸尘

Hence, the wavelength of the gamma rays scattered at 90 degrees to the incident beam is 4.86鈥塸尘.

03

The photon energy of the ray scattered in the direction.

(c)

The scattered photons have energy equal to as follows;

E'=E位位'=(0.511鈥夆�塎别痴)2.434.86=0.255鈥塎别痴

Hence, the photon energy for the ray scattered in the direction is0.255鈥塎别痴.

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