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

`t_(1/2)=6 h`

Step-by-step 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=(ln(2))/(t_(1/2))`

So we have:

`\lambda=(ln(A/A_(0)))/(t)`

`(ln(2))/(t_(1/2))=(ln(A/A_(0)))/(t)`

`t_(1/2)=(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!