Answer to Question #205431 in Atomic and Nuclear Physics for Tristan Gibson

Question

An important radioisotope for industrial and medical applications is 60Co with a half life of 5.2 years and a molar mass of 60 grams/mole. What minimum initial mass of 60Co is required for a sealed cource of 60Co to have an activity of 10 Ci after 30 months where 1Ci=3.7x1010 Bq. 

Answer 1

Convert from Ci to Bq: 10 Ci is 3.7·10¹¹ Bq.

Determine decay constant:

$$\lambda=\frac{\ln2}{t}=0.0111\text{ month}^{-1}.$$

Find initial activity:

$$A=A_0e^{-\lambda t},\\\space\\ A_0=\frac{A}{e^{-\lambda t}}=5.16·10^{11}\text{ Bq}.$$

Activity can be expressed as a product of decay constant and number of particles:

$$A=\lambda N.$$

Find initial N:

$$N_0=\frac{A_0}{\lambda}=1.22·10^{22}.$$

Find the amount of substance:

$$n_0=\frac{N_0}{N_A}=0.0203\text{ mol}.$$

Find the mass:

$$m_0=n_o\Mu=1.22\text{ g}.$$