A sample which has half life of 10^{33} year, if initial number of nuclei of sample is 26 × 10^{24}

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13.Nuclei

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A sample which has half life of $10^{33}$ year, if initial number of nuclei of the sample is $26 \times 10^{24}$. Then the number of nuclei decayed in $1$ year is ........... $ \times 10^{-7}$

A

$1.82$

B

$182$

C

$18.2$

D

$1820$

(AIIMS-2019)

Solution

The number of nuclei decayed in $1$ year is calculated as,

$-\frac{d N}{d t}=\lambda N$

$-d N=\frac{\ln 2}{T} \times N \times d t$

$=\frac{0.7}{10^{33}} \times 26 \times 10^{24} \times 1$

$=18.2 \times 10^{-7}$

Standard 12

Physics

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