Question:
A freshly prepared radioactive source of half-life 2 h emits radiation of intensity which is 64 times the permissible safe level. Calculate the minimum time after which it would be possible to work safely with this source.
A freshly prepared radioactive source of half-life 2 h emits radiation of intensity which is 64 times the permissible safe level. Calculate the minimum time after which it would be possible to work safely with this source.
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A freshly prepared radioactive source of half-life 2 h emits radiation of intensity which is 64 times the permissible safe level. Calculate the minimum time after which it would be possible to work safely with this source.
Updated On: Apr 15, 2026
- 12 h
- 24 h
- 6 h
- 130 h
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The Correct Option is A
Solution and Explanation
Step 1: Concept
The activity reduces to $1/2^n$ of the original after $n$ half-lives.
Step 2: Analysis
To reach the safe level, intensity must reduce to $1/64$ of its current value. $$\frac{1}{2^n} = \frac{1}{64} \Rightarrow 2^n = 2^6 \Rightarrow n = 6$$
Step 3: Calculation
Total time $t = n \times T = 6 \times 2 \text{ h} = 12 \text{ h}$.
Final Answer: (A)
The activity reduces to $1/2^n$ of the original after $n$ half-lives.
Step 2: Analysis
To reach the safe level, intensity must reduce to $1/64$ of its current value. $$\frac{1}{2^n} = \frac{1}{64} \Rightarrow 2^n = 2^6 \Rightarrow n = 6$$
Step 3: Calculation
Total time $t = n \times T = 6 \times 2 \text{ h} = 12 \text{ h}$.
Final Answer: (A)
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