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Question:

A freshly prepared radioactive source of half-life 2h 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.

12 h

24 h

6 h

130 h

Solution:

The intensity of radioactive decay after time t is I(t)=I₀e⁻ᵏᵗ
Hence half life is given by τ=ln2/k=2h ⇒k=ln2/2h
The intensity must drop to 1/64 of its present intensity to work safely.
Hence, I₀/64=I₀e⁻ᵗ(ln2/2)
⇒t(ln2/2h) = ln64
⇒t=12h