Question

The count rate of a radioactive source decreases from 1600 counts per minute to 400 counts per minute in 12 hours. What is the half-life of the source?

Answer 1

Answer:

$t_{1/2}=6 h$

Explanation:

Let's use the decay equation.

$A=A_{0}e^{-\lambda t}$

Where:

• A is the activity at t time
• A₀ is the initial activity
• λ is the decay constant

We know that $\lambda=\frac{ln(2)}{t_{1/2}}$

So we have:

$\lambda=\frac{ln(A/A_{0})}{t}$

$\frac{ln(2)}{t_{1/2}}=\frac{ln(A/A_{0})}{t}$

$t_{1/2}=\frac{t*ln(2)}{ln(A/A_{0})}$

$t_{1/2}=6 h$

Therefore, the half-life of the source is 6 hours.

I hope it helps you!