Modern Physics 5 Question 1

1. Half lives of two radioactive nuclei A and B are 10 minutes and 20 minutes, respectively. If initially a sample has equal number of nuclei, then after

60 minutes, the ratio of decayed numbers of nuclei A and B will be

(Main 2019, 12 April II)

(a) 3:8

(b) 1:8

(c) 8:1

(d) 9:8

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Answer:

Correct Answer: 1. (d)

Solution:

  1. For substance A, half-life is 10min, so it decays as

10minN0A1610minN0A3210minN0A64

For substance A, number of nuclei decayed in 60min is

N0AN0A64=63N0A64

Similarly, for substance B, half-life is 20min, so it’s decay scheme is

N0B20minN0B220minN0B420minN0B8

So, number of nuclei of B decayed in 60min is

N0BN0B8=78N0B

Hence, ratio of decayed nuclei of A and B in 60min is

6364N0A78N0B=98[N0A=N0B]

Alternate Solution

Number of active nuclei remained after 60min can also be calculated as

N=N2T/t1/2

where, T=60min

So, for nuclei A,

N0A=N0A26010=N0A26=N0A64

Similarly, for nuclei B,

N0B=N0B26020=N0B23=N0B8



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