Half life of radium is 1620 years. How many r | vedclass

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Question

Given, Half-life, $T_{\frac{1}{2}}=\frac{0.693}{\lambda}$

$\overline{2}$

$\Rightarrow \lambda=\frac{0.693}{1620 	imes 365 	imes 24} \mathrm{hr

Vedclass · Accepted Answer

$3.23 	imes 10^{15}$

Vedclass · Answer

Given, Half-life, $T_{\frac{1}{2}}=\frac{0.693}{\lambda}$

$\overline{2}$

$\Rightarrow \lambda=\frac{0.693}{1620 	imes 365 	imes 24} \mathrm{hr}^{-1}$

In time $(t=5$ hours $), \lambda t=\frac{0.693 	imes 5}{1620 	imes 365 	imes 24}=2.44 	imes 10^{-7}$

$N_{o}=\frac{m N_{A}}{M_{o}}=\frac{5 	imes\left(6.023 	imes 10^{23}ight)}{233}=1.292 	imes 10^{22}$ nuclei

Number of radium nuclei decay in 5 hours is $\left(N_{o}-Night)=N_{0}\left(1-e^{-\lambda t}ight)$

$\left(N_{o}-Night)=1.292 	imes 10^{22}\left(1-e^{-2.44 	imes 10^{-7}}ight)$

$\left(N_{o}-Night)=3.23 	imes 10^{15}$

Number of radium nuclei decay in 5 hours is $3.23 	imes 10^{15}$ nuclie

Half life of radium is $1620$ years. How many radium nuclei decay in $5$ hours in $5\, gm$ radium? ( Atomic weight of radium $= 223$)

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