Physics and Engineering of Radiation Detection

58 Chapter 1. Properties and Sources of Radiation

Problems

1.Compute the de Broglie wavelength of an electron moving with a velocity of

2. 5 × 108 ms−^1.

2.Compare the de Broglie wavelength of a proton moving at 0. 9 c,cbeing the

velocity of light in vacuum, with the wavelength of x-rays (10−^10 m).

3.Scintillators are the materials that produce light when they are exposed to

radiation. Most scintillators used to build detectors produce light in blue and

green regions of the electromagnetic spectrum with mean wavelengths of 475

nmand 510nmrespectively. Compute the energies and frequencies associated

with these photons.

4.What is the minimum de Broglie wavelength of an electron accelerated in a 40

kVx-ray tube.

5.Write down the decay equations for the following radionuclides.

22

11 Na(β),

60

27 Co(EC),

127

55 Cs(β),

241

95 Am(α),

252

98 Cf(α)

6.A newly produced radioactive decay sample has an initial activity of 200MBq.

Compute its decay constant, half life, and mean life if after 5 days its activity

decreases to 150MBq.

7.Show that for a massive nucleus undergoingα-decay, the energy of the emitted

αparticle is approximately given by

Tα≈

[

A− 4

4

]

Qα,

whereAis the mass number of the parent nucleus.

8.Compute theQ-values andα-particle energies for plutonium-239, americium-

243, and bismuth-214.

9.Verify thatFe-55 can decay by electron capture.

10.Determine ifPb-187 can decay by bothαandβemissions.

11.Calculate the rate ofα-particle emissions from a 5mgsample of^23994 Pu.

12.The initial activity of a radioactive sample is found to be 1. 5 mCi.Findits

decay constant if after 3 years its activity decreases to 1mC.

13.A radioactive element decays with a half life of 43 days. If initially there are

2.5 moles of this element in a sample, how many of its atoms will be left in the

sample after 43 days, 6 months, and 1 year.

14.Estimate the mean life of a radionuclide that has decayed by 75% in 24 hours.

15.The mean life of a radionuclide is 15 days. What fraction of it will remain

radioactive after 30 days?

16.Compute the ratio of the number of atoms decayed to the initial number of

atoms of a radioactive substance after 4.5 half lives.