Question

Find the probability that the nucleus of 87Ra^221 undergoes decay after three half-lives, if its a radioactive substance which has a half-life of 6 days.

(a) \(\frac {1}{6}\)

(b) \(\frac {3}{2}\)

(c) \(\frac {5}{6}\)

(d) \(\frac {1}{2}\)

The question was asked in examination.

This key question is from Nucleus in chapter Nucleus of Physics – Class 12

Answer 1

The correct answer is (c) \(\frac {5}{6}\)

Best explanation: After one-half life, \(\frac {N_0}{2}\) sample remains and \(\frac {N_0}{2}\) decays.

After three half-lives, \(\frac {N_0}{6}\) sample remains and \(\frac {5N_0}{6}\) decays.

Hence the probability that a nucleus undergoes decay after two half-lives is \(\frac {5}{6}\).