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At a given instant there are 25 % undecayed radioactive nuclei

Question

Medium

Solving time: 3 mins

At a given instant there are $25%$ undecayed radioactive nuclei in a sample. After $10 s$ the number of undecayed nuclei reduces to $12.5%$ . Calculate
(a) mean life of the nuclei,
(b) the time in which the number of undecayed nuclei will further reduce to $6.25%$ of the reduced number.

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Exam:

JEE Advanced 1996

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Daniel Discussed

At a given instant there are

25%

undecayed radioactive nuclei in a sample. After

10 s

the number of undecayed nuclei reduces to

12.5%

. Calculate
(a) mean life of the nuclei,
(b) the time in which the number of undecayed nuclei will further reduce to

6.25%

of the reduced number.

9 mins ago

Discuss this question LIVE

9 mins ago

Text solutionVerified

(a) In

10 s

, number of nuclei has been reduced to half

(25%

12.5%) .

Therefore, its half-life is

t_{1/2} = 10 s

Relation between half-life and mean life is

t_{mean} = \frac{t _{1/2}}{l n ( 2 )} = \frac{10}{0.693} s t_{mean} = 14.43 s

(b) From initial

100%

to reduction till

6.25%

, it takes four half lives.

100% ⟶ t_{1/2} 50% ⟶ t_{1/2} 25% ⟶ t_{1/2} 12.5% ⟶ t_{1/2} 6.25% ∴ t = 4 t_{1/2} = 4 (10) s = 40 s

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Question Text	At a given instant there are $25%$ undecayed radioactive nuclei in a sample. After $10 s$ the number of undecayed nuclei reduces to $12.5%$ . Calculate (a) mean life of the nuclei, (b) the time in which the number of undecayed nuclei will further reduce to $6.25%$ of the reduced number.
Topic	Nuclei
Subject	Physics
Class	Class 12
Answer Type	Text solution:1
Upvotes	62

At a given instant there are $25%$ undecayed radioactive nuclei in a sample. After $10 s$ the number of undecayed nuclei reduces to $12.5%$ . Calculate
(a) mean life of the nuclei,
(b) the time in which the number of undecayed nuclei will further reduce to $6.25%$ of the reduced number.

Text solutionVerified

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At a given instant there are 25% undecayed radioactive nuclei in a sample. After 10 s the number of undecayed nuclei reduces to 12.5%. Calculate(a) mean life of the nuclei,(b) the time in which the number of undecayed nuclei will further reduce to 6.25% of the reduced number.

Text solutionVerified

Questions from JEE Advanced 1996 - PYQs

Practice questions from Nuclei in the same exam

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Practice questions on similar concepts asked by Filo students

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Previous year question papers

At a given instant there are $25%$ undecayed radioactive nuclei in a sample. After $10 s$ the number of undecayed nuclei reduces to $12.5%$ . Calculate
(a) mean life of the nuclei,
(b) the time in which the number of undecayed nuclei will further reduce to $6.25%$ of the reduced number.