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13.Nuclei
hard
${ }^{198} {Au}$ નો અર્ધઆયુષ્ય સમય $3 \,days$ છે. જો ${ }^{198} {Au}$ નું આણ્વિય દળ $198\, {g} / {mol}$ હોય તો ${ }^{198} {Au}$ ના $2 \,{mg}$ દળની એક્ટિવિટી ..... $\times 10^{12}\,disintegration/second$ હશે.
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
