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The half-life of a radioactive substance is 30 minutes. The time (in minute) taken between 40% decay and 85% decay of the same radioactive substance is:

A

15

B

30

C

45

D

60

Step-by-Step Solution

  1. Understand Decay vs. Remaining: Radioactive decay calculations are based on the amount of substance remaining (NN), not the amount decayed.
  • At 40% decay, the amount remaining N1=(100−40)%=60%N_1 = (100 - 40)\% = 60\% of the initial amount N0N_0.
  • At 85% decay, the amount remaining N2=(100−85)%=15%N_2 = (100 - 85)\% = 15\% of the initial amount N0N_0.
  1. Analyze the Change: Compare the remaining amounts N1N_1 and N2N_2. N1N2=60%15%=4\frac{N_1}{N_2} = \frac{60\%}{15\%} = 4
  • Since 4=224 = 2^2, the substance has reduced by a factor of 4, which corresponds to exactly 2 half-lives.
  • Sequence: 60%→T1/230%→T1/215%60\% \xrightarrow{T_{1/2}} 30\% \xrightarrow{T_{1/2}} 15\%.
  1. Calculate Time:
  • Given half-life (T1/2T_{1/2}) = 30 minutes.
  • Time taken = 2×T1/2=2×30 min=60 min2 \times T_{1/2} = 2 \times 30 \text{ min} = 60 \text{ min}.
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