A sealed radioactive laboratory source initially has activity 320 kBq. Laboratory rules permit direct handling only after the activity becomes 10 kBq or less. If the half-life is 2 h, find the minimum waiting time in hours.
Physics · Nuclear physics · radioactivity and law of decay
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Question

A sealed radioactive laboratory source initially has activity 320 kBq. Laboratory rules permit direct handling only after the activity becomes 10 kBq or less. If the half-life is 2 h, find the minimum waiting time in hours.

Physics · Nuclear physics · radioactivity and law of decay

G1 Physics · Accepted Answer

Required activity reduction: 320 ÷ 10 = 32 = 2⁵. Thus the source must pass through five half-lives. Time required: t = 5×2 h = 10 h. At 10 h the activity is exactly 10 kBq, satisfying the stated limit. Hence N = 10.