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13.Nuclei
hard
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
