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satela [25.4K]
2 years ago
12

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

alf-life of the source?
Physics
1 answer:
kirill115 [55]2 years ago
4 0

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!

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