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A radioactive sample S1 having the activity A1 has twice the no of nuclei as another sample S2 of activity A2 .If A2=4A1 then the ratio of half life of S1 to the half of S2 is? a)2 b)0.5 c)8 d)0.125?
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Solution:

Given that,
Activity of sample S1 = A1
Activity of sample S2 = A2 = 4A1
Number of nuclei in S1 = 2x (number of nuclei in S2)

Let us assume that the number of nuclei in sample S2 is N2.
Then, the number of nuclei in sample S1 would be 2N2.

Now, we know that,
Activity = λN, where λ is the decay constant and N is the number of nuclei.

Therefore, we can write,
A1 = λN1
4A1 = λN2

Also, we know that the decay constant is related to the half-life (t1/2) as follows:
t1/2 = ln(2)/λ

Hence, we can write the ratio of the half-life of S1 to the half-life of S2 as follows:

(t1/2)S1 / (t1/2)S2 = (ln(2)/λ)S1 / (ln(2)/λ)S2
= λS2 / λS1
= (4A1 / N2) / (A1 / 2N2)
= 8

Therefore, the ratio of half-life of S1 to the half-life of S2 is 8.

Answer: c) 8
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A radioactive sample S1 having the activity A1 has twice the no of nuclei as another sample S2 of activity A2 .If A2=4A1 then the ratio of half life of S1 to the half of S2 is? a)2 b)0.5 c)8 d)0.125?
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A radioactive sample S1 having the activity A1 has twice the no of nuclei as another sample S2 of activity A2 .If A2=4A1 then the ratio of half life of S1 to the half of S2 is? a)2 b)0.5 c)8 d)0.125? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A radioactive sample S1 having the activity A1 has twice the no of nuclei as another sample S2 of activity A2 .If A2=4A1 then the ratio of half life of S1 to the half of S2 is? a)2 b)0.5 c)8 d)0.125? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A radioactive sample S1 having the activity A1 has twice the no of nuclei as another sample S2 of activity A2 .If A2=4A1 then the ratio of half life of S1 to the half of S2 is? a)2 b)0.5 c)8 d)0.125?.
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