A radioactive nucleus can decay by two different processes. Half-… - Vidyadip

MCQ

A radioactive nucleus can decay by two different processes. Half-life for the first process is $3.0\, hours$ while it is $4.5\, hours$ for the second process. The effective half- life of the nucleus will be $.........\,hours.$

A
$3.75$
B
$0.56$
C
$0.26$
✓
$1.80$

✓

Answer

Correct option: D.

$1.80$

d
$\lambda_{\text {eq }}=\lambda_{1}+\lambda_{2}$

$\frac{\ln 2}{\left( t _{1 / 2}\right)_{ eq }}=\frac{\ln 2}{\left( t _{1 / 2}\right)_{1}}+\frac{\ln 2}{\left( t _{1 / 2}\right)_{2}}$

$\left( t _{1 / 2}\right)_{ eq }=\frac{\left( t _{1 / 2}\right)_{1} \times\left( t _{1 / 2}\right)_{2}}{\left( t _{1 / 2}\right)_{1}+\left( t _{1 / 2}\right)_{2}}$

$=\frac{3 \times 4.5}{3+4.5}=\frac{3 \times 4.5}{7.5}=\frac{3 \times 3}{5}=1.8 \; hr$

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