Half life of $^{238}\text{U}_{92}$against$\alpha$ decay is $4.5 \times 10^{9}$years. Calculate the activity of Ig sample of$^{238}\text{U}_{92}$? Given Avogadro's number $= 6 \times 10^{26}$atoms/kmol.
CBSE OUTSIDE DELHI - SET 1 EAST 2016
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Activity, R = λN
$ = \frac{0.693}{\text{T}_{1/2}}\text{N}$
Activity ( R ) $ = \frac{0.693}{1.42\times10^{17}}\times\text{N}$
Number of nuclei present in 1 gram sample of $^{238}_{92}\text{U} = 2503\times10^{20}$
$\Rightarrow\text{R} = \frac{0.693}{1.42\times10^{17}}\times\frac{6.0\times10^{26}}{238\times10^{3}}\text{s}^{-1}$
$ = 1.23\times10^{4}\text{s}^{-1}$.
$ = \frac{0.693}{\text{T}_{1/2}}\text{N}$
Activity ( R ) $ = \frac{0.693}{1.42\times10^{17}}\times\text{N}$
Number of nuclei present in 1 gram sample of $^{238}_{92}\text{U} = 2503\times10^{20}$
$\Rightarrow\text{R} = \frac{0.693}{1.42\times10^{17}}\times\frac{6.0\times10^{26}}{238\times10^{3}}\text{s}^{-1}$
$ = 1.23\times10^{4}\text{s}^{-1}$.
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