Suggested+Solutions+to+Amount+of+Radioactive+Material+(number+of+nuclei,+number+of+moles,+weight)+and+the+Law+of+Radioactive+Decay

Exercises with Amount of Radioactive Material (number of nuclei, number of moles, weight) and the Law of Radioactive Decay
 * 1: **
 * 1) 3.2 • 10 8  Bq
 * 2) 383 Bq
 * 3) 2.3 • 10 9  Bq
 * 4) 8.0 • 10 4  Bq


 * 2: **
 * 1) 1.77 • 10 13  atoms.
 * 2) 2.00 • 10 11  atoms.

 **3:** 2.40 g 60 Co.

<span style="font-family: 'Times New Roman','serif'; font-size: 16px;"> **4:**
 * 1) <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">2.53 • 10 5 <span style="font-family: 'Times New Roman','serif'; font-size: 16px;"> Bq.
 * 2) <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">7.21 years = 7 years and 76.7 days.

<span style="font-family: 'Times New Roman','serif'; font-size: 16px;">The mass of 99m <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">Tc is 20.5 ng. After one week 28 half-lives will have past, and the activity will be the following:
 * <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">5: **

<span style="font-family: 'Times New Roman','serif'; font-size: 16px;">D = D 0<span style="font-family: 'Times New Roman','serif'; font-size: 16px;"> • (½) 28 =4•0 7 Bq•(½) 28 <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">=0.15 Bq.

<span style="font-family: 'Times New Roman','serif'; font-size: 16px;">Approximately all 99m <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">Tc has disintegrated and turned into 99 <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">Tc. The number of 99 <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">Tc atoms will therefore be the same as the original number of 99m <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">Tc atoms.

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


 * <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">6: **
 * 1) <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">1 g natural Lu contains 0.0259 g 176 <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">Lu, with a half-life equal to 3.8 • 10 10 <span style="font-family: 'Times New Roman','serif'; font-size: 16px;"> years, which gives A = 51 Bq
 * 2) <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">There are two naturally occurring radioisotopes of Sm, 147 <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">Sm and 148 <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">Sm, which gives A = 127.24 Bq + 0.001 Bq = 127 Bq.

<span style="font-family: 'Times New Roman','serif'; font-size: 16px;">3002 kg
 * <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">7: **


 * <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">8: **
 * 1) <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">18.5 kg
 * 2) <span style="font-family: 'Times New Roman','serif'; font-size: 16px;"> After 2.455 • 10 5 <span style="font-family: 'Times New Roman','serif'; font-size: 16px;"> years it will be 2.299 • 10 8 <span style="font-family: 'Times New Roman','serif'; font-size: 16px;"> Bq 238 <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">U left, which is equal to 18.49 kg.