SATHEE: Atoms And Nuclei Question 411

Atoms And Nuclei Question 411

Question: The ratio of half-life times of two elements A and B is $\frac{T_{A}}{T_{B}}$ . The ratio of respective decay constant $\frac{λ_{A}}{λ_{B}},$ is

Options:

A) $T_{B} / T_{A}$

B) $T_{A} / T_{B}$

C) $\frac{T_{A} + T_{B}}{T_{A}}$

D) $\frac{T_{A} - T_{B}}{T_{A}}$

Show Answer

Answer:

Correct Answer: A

Solution:

$T_{1 / 2} = \frac{I n 2}{λ} ∴ λ = \frac{I n 2}{T_{1 / 2}}$
$\Rightarrow λ_{A} = \frac{I n 2}{T_{A}}, λ_{B} = \frac{I n 2}{T_{B}} \Rightarrow \frac{λ_{A}}{λ_{B}} = \frac{T_{B}}{T_{A}} .$

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