Question

The nucleid ratio of tritium and hydrogen in a sample of water is $9.0\times {10}^{-18}:1$. Tritium undergoes decay with a half-life period of 6.93 years. If 10 g of such a sample was taken for a study, after 46 years of collection, the nearest integer value of log $N$ is: (Given log$6.023=0.78$)

Answer 1

18 g of $H_{2}O$ has 2N hydrogen atoms in it and $H^3:H^1$ is $9.0\times {10}^{-18}:1$
18 g of $H_{2}O$ contains $(9.0\times {10}^{-18}\times 6.023\times {10}^{23}\times 2)H^3$ atoms
10 g of $H_{2}O$ contains $(9.0\times {10}^{-18}\times 6.023\times {10}^{23}\times 2)\times \frac{10}{18}$$=6.023\times {10}^6$ atoms of $H^3$
$t=\frac{2.303}{k}log\frac{N_o}{N}$
$46=\frac{2.303\times 6.93}{0.693}log\frac{6.023\times {10}^6}{N}$
$log\frac{6.023\times {10}^6}{N}=\frac{46\times 0.693}{2.303\times 6.93}=2$
$log(6.023\times {10}^6)=2+logN$
$logN=4.78\approx 5$