A sample of radioactive material A , that has an activity of 10, mCi, (1, Ci = 3.7 × 10^{10}, decay

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13.Nuclei

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A sample of radioactive material $A$, that has an activity of $10\, mCi\, (1\, Ci = 3.7 \times 10^{10}\, decays/s)$, has twice the number of nuclei as another sample of different radioactive material $B$ which has an activity of $20\, mCi$. The correct choices for half-lives of $A$ and $B$ would then be respectively

A

$5$ days and $10$ days

B

$10$ days and $40$ days

C

$20$ days and $5$ days

D

$20$ days and $10$ days

(JEE MAIN-2019)

Solution

Activity $=\lambda$ (number of atoms)

$10=\lambda_{A} N_{A}$ ….. $(1)$

$20=\lambda_{B} N_{B}$ ….. $(2)$

$N_{A}=2 N_{B}$ ….. $(3)$

Solving we get, $\frac{\lambda_{A}}{\lambda_{B}}=\frac{1}{4}$

Standard 12

Physics

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