The half-life of a given radioactive nucleus is 200 days. The mean li…

The correct answer is Option (1) → 288 days

The mean life \( \tau \) is the reciprocal of the decay constant, and the half-life is \( T_{1/2} = 0.693/\lambda \). So the two are related by

    \( \displaystyle \tau = \frac{1}{\lambda} = \frac{T_{1/2}}{0.693} = 1.44\,T_{1/2} \)

    \( \displaystyle \tau = \frac{200}{0.693} \approx 288\,\mathrm{days} \)

Note: This question is from the pre-rationalised NCERT book (2022-23). The topic was removed from the latest NCERT book (2026-27), and it also appears to be out of the CUET 2026 syllabus.

NCERT (Pre-rationalised edition, 2022-23):
Law of Radioactive Decay – “… One measure is the half-life T_1/2 of a radionuclide, which is the time at which both N and R have been reduced to one-half their initial values. The other measure is the mean life τ, which is the time at which both N and R have been reduced to e^–1 of their initial values.”

Law of Radioactive Decay – “… We summarise these results with the following:

    \( \displaystyle T_{1/2} = \frac{\ln 2}{\lambda} = \tau \ln 2 \qquad (13.18) \)”