Half-life of { }^{198} {Au} is 3 ,days. If atomic weight of { }^{198} {Au} is 198, {g} / {mol} then

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13.Nuclei

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The half-life of ${ }^{198} {Au}$ is $3 \,days.$ If atomic weight of ${ }^{198} {Au}$ is $198\, {g} / {mol}$ then the activity of $2 \,{mg}$ of ${ }^{198} {Au}$ is ..... $\times 10^{12}\,disintegration/second$

A

$2.67$

B

$16.18$

C

$6.06$

D

$32.36$

(JEE MAIN-2021)

Solution

$A =\lambda N$

$\lambda=\frac{\ln 2}{ t _{1 / 2}}=\frac{\ln 2}{3 \times 24 \times 60 \times 60} sec ^{-1}=2.67 \times 10^{-6} sec ^{-1}$

$N =$ Number of atoms in $2 \;mg \;Au$

$=\frac{2 \times 10^{-3}}{198} \times 6 \times 10^{23}=6.06 \times 10^{15}$

$A=\lambda N =1.618 \times 10^{13}=16.18 \times 10^{12} dps$

Standard 12

Physics

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