Solutions 3

Amount of radioactive material (number of nuclei <-> number of moles <-> weigth) and law of radioactive decay

1:

1. 3.2 <span style="background-color: navy; color: white;" />• 10⁸ Bq
2. 383 Bq
3. 2.3 <span style="background-color: navy; color: white;" />• 10⁹ Bq
4. 8 <span style="background-color: navy; color: white;" />• 10⁴ Bq

2:

1. 1.78 <span style="background-color: navy; color: white;" />• 10¹³ atoms.
2. 2 <span style="background-color: navy; color: white;" />• 10¹¹ atoms.

3: 2.40 g ⁶⁰Co.

4:

1. 2.53 <span style="background-color: navy; color: white;" />• 10⁵ Bq.
2. 7.19 years = 7 years and 68 days.

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

D = D₀ <span style="background-color: navy; color: white;" />• (½)²⁸ = 4 <span style="background-color: navy; color: white;" />• 10⁷ Bq <span style="background-color: navy; color: white;" />• (½)²⁸ = 0.15 Bq.

All ^99mTc has disintegrated and turned into ⁹⁹Tc. The number of ⁹⁹Tc atoms will therfore be the same as the original number of ^99mTc atoms.

N = = = 1,25 <span style="background-color: navy; color: white;" />• 10¹² atomer

 The activity will then be: D = λN = 1.05 <span style="background-color: navy; color: white;" />• 10^-13 s^-1 <span style="background-color: navy; color: white;" />• 1.25 <span style="background-color: navy; color: white;" />• 10¹² = 0.13 Bq.

6:

1. 1 g nat-Lu contains 0.0259 g ¹⁷⁶Lu, which has a half-life of 3.8<span style="background-color: navy; color: white;" />•10¹⁰ years. This gives D = 51 Bq
2. There are two naturally occuring Sm radioisotopes, ¹⁴⁷Sm and ¹⁴⁸Sm, which gives D = 127.24 Bq + 0.001 Bq = 127 Bq.

7: 3002 kg

8:

1. 18.5 kg
2.  After 2.455<span style="background-color: navy; color: white;" />•10⁵ years it remains 2.299<span style="background-color: navy; color: white;" />•10⁸ Bq ²³⁸U,which is equal to18.49 kg.