Question

A radioactive sample had an initial activity of 56 dpm. After 69.3 minutes, it was found to have an activity of 28 dpm. Find the number of atoms in a sample that has an activity of 100 dpm.

• A. 693
• B. 100
• C. 1000
• D. 10,000

Answer 1

The correct option is D 10,000

Given
$N_o=\frac{56}{\lambda }$
$N_{69.3}=\frac{28}{\lambda }$
$N_t=\frac{100}{\lambda }$
$\lambda \times 69.3=ln\frac{56}{28}$
$\lambda =\frac{ln2}{69.3}$
$=0.01$
$\frac{100}{0.01}=N_t$
$N_t={10}^4$