Atoms And Nuclei Question 377

Question: The activity of a radioactive sample is A1 at time t1 and A2 at time t2 . If τ is average life of sample then the number of nuclei decayed in time ( t2−t1 ) is

Options:

A) A1t1−A2t2

B) (A2−A1)2τ

C) (A1−A2)(t2−t1)

D) (A1−A2)τ.

Show Answer

Answer:

Correct Answer: D

Solution:

  • Let N0 be the initial number of nuclei, then

    N1=N0e−λt1

    and N2=N0e−λt2
    ∴

    Number of nuclei decayed =N1−N2 =N0(e−λt1−e−λt2)=A0λ(e−λt1−e−λt2)

    =A1−A2λ=(.A1−A2)τ.

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