Question
Half-lives of two radioactive elements A and B are 20 minutes and 40 minutes, respectively. Initially, the samples have equal number of nuclei. After 80 minutes, the ratio of decayed numbers of A and B nuclei will be:
-
1: 16
-
4 : 1
-
1: 4
-
5: 4
Solution
D.
5: 4
Given 80 min = 4 half-lives of A = 2 half-lives of B.
Let the initial number of nuclei in each sample be N.
For radioactive element A,
NA after 80 min = N/24
⇒ Number of A nuclides decayed =
For radioactive element B,
NB after 80 min = N/22
⇒ Number of B nuclides decayed
=
therefore, the ratio of decayed numbers of A and B nuclei will be
