Find the probability that the nucleus of 87Ra221 undergoes decay after three half-lives if it’s a radioactive substance that has a half-life of 6 days.a)1/6b)5/6c)7/8d)1/2Correct answer is option 'C'. Can you explain this answer?

Question

Find the probability that the nucleus of 87Ra221 undergoes decay after three half-lives if it&rsquo;s a radioactive substance that has a half-life of 6 days.a)1/6b)5/6c)7/8d)1/2Correct answer is option 'C'. Can you explain this answer?

Answer

After one half-life, N/2 sample remains and N/2 decays. After two half-lives, N/4 sample remains and N/4 decays out of the remaining N/2 sample. After three half-lives, N/8 sample remains and N/8 sample decays out of the remaining N/4 sample.
So, after three half-lives, in total, N/2 + N/4 + N/8 = 7N/8 decay happens. Hence, the probability that a nucleus undergoes decay after three half-lives is 7/8.

Answer

If the half-life of a nucleus is given, we can find the probability of decay after a certain number of half-lives by using the formula:

P = (1/2)^n

where P is the probability of decay and n is the number of half-lives. In this case, we are looking for the probability of decay after three half-lives, so n = 3.

P = (1/2)^3 = 1/8

Therefore, the probability that the nucleus of 87Ra221 undergoes decay after three half-lives is 1/8.

Similar Class 12 Doubts

what is the half life of radioactive substance if 87.5% of any given amount of the substance disintegrate in 40 minutes

Half-lives of two radioactive substances A and B are respectively 20 minutes and 40 minutes.Initially, the samples of A and B have equalnumber of nuclei. After 80 minutes the ratio ofremaining numbers of A and B nuclei is [1998]

Half life of a radioactive substance is 10 second. Then undecayed nuclei of the substance will reduce to 6.25% of their value at t = 0 in a time of

At a given instant,there are 25 percent undecayed radioactive nuclei in a sample. After 8 sec the number of undecayed nuclei reduced to 12.5 percent.The time after which the number of undecayed nuclei will further reduce to 6.25 percent of the reduced number is____sec?

Binding energy per nucleon is the ratio of

Top Courses for Class 12

Suggested Free Tests

Related Content

Schools

Competitive Examinations

Quick Access Links

Technical Exams