Question

If the half-life of a radioactive material is 5 days, then the ratio of the number of atoms disintegrated in 10 and 15 days is:

• A. 6:7
• B. 2:3
• C. 3:8
• D. 5:7

Hint:

Disintegrated atoms = initial - remaining.
Use $N = N_0 2^{-t/T_{1/2}}$.
Convert fractions to common denominator for ratio.
Check time multiple of half-life carefully.

Answer 1

The Correct Option is A

• Fraction remaining after time $t$: $N = N_0 2^{-t/T_{1/2}}$.
• At 10 days: $N_{10} = N_0 2^{-10/5} = N_0 / 4$, disintegrated: $N_0 - N_{10} = 3 N_0 / 4$.
• At 15 days: $N_{15} = N_0 2^{-15/5} = N_0 / 8$, disintegrated: $7 N_0 / 8$.
• Ratio: $(3/4) : (7/8) = 6:7$.
• Hence ratio = 6:7.