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Exercises with Amount of Radioactive Material (number of nuclei, number of moles, weight) and the Law of Radioactive Decay
1:
  1. 3.2 • 108 Bq
  2. 383 Bq
  3. 2.3 • 109 Bq
  4. 8.0 • 104 Bq

2:
  1. 1.77 • 1013 atoms.
  2. 2.00 • 1011 atoms.

3:
2.40 g 60Co.

4:
  1. 2.53 • 105 Bq.
  2. 7.21 years = 7 years and 76.7 days.

5:
The mass of 99mTc is 20.5 ng. After one week 28 half-lives will have past, and the activity will be the following:

D = D0 • (½)28=4•07 Bq•(½)28=0.15 Bq.

Approximately all 99mTc has disintegrated and turned into 99Tc. The number of 99Tc atoms will therefore be the same as the original number of 99mTc atoms.

N=\frac{D}{\lambda} \rightarrow \frac{4\cdot 10^{7}Bq}{3.21\cdot 10^{-5}s^{-1}}=1.25\cdot 10^{12}\,atoms

6:
  1. 1 g natural Lu contains 0.0259 g 176Lu, with a half-life equal to 3.8 • 1010 years, which gives A = 51 Bq
  2. There are two naturally occurring radioisotopes of Sm, 147Sm and 148Sm, which gives A = 127.24 Bq + 0.001 Bq = 127 Bq.

7:
3002 kg

8:
  1. 18.5 kg
  2. After 2.455 • 105 years it will be 2.299 • 108 Bq 238U left, which is equal to 18.49 kg.