Question

$4\times {10}^{23}$ tritium atoms are contained in a vessel. The half-life of decay of tritium nuclei is 12.3 y. Find (a) the activity of the sample, (b) the number of decays in the next 10 hours (c) the number of decays in the next 6.15 y.

Answer 1

Given N$=4\times {10}^{23}$

$t_{\frac{1}{2}}=12.3\text{years}$

$\text{Activity}=\frac{dN}{dt}$

$\lambda n=\frac{0.693}{t_{\frac{1}{2}}}N$

$=\frac{0.693}{12.3}\times 4\times {10}^{23}\text{dis/ year}$

$=\frac{0.693\times 4\times {10}^{28}}{12.3\times 3600\times 24\times 365}\text{dis / sec}$

$=7.146\times {10}^{14}\text{dis / sec}$

(b) $\frac{dN}{dt}=7.146\times {10}^{14}$

$\text{No. of decays in next 10 hrs}$

=$7.146\times {10}^{14}\times 10\times 3600$

=$257.256\times {10}^{17}=2.75\times {10}^{19}$

(c)$\text{N}={\text{N}}_0{e}^{-\lambda t}=2.82\times {10}^{28}$

=$\text{No. of atoms remained}$

$\text{No. of atoms disintegrated}$

=$(4-2.82)\times {10}^{28}=1.18\times {10}^{28}$