Question

The nucleidic ratio of${}_1{H}^3$ to ${}_1{H}^1$ in a sample of water is $8.0\times {10}^{18}:1$. Tritium undergoes decay with a half period of 12.3 year.How many tritium atoms would 10.0g of such a sample contains 40 ycar after the original sample is collected?

• A. $1.686\times {10}^6$ atoms
• B. $6.624\times {10}^5$ atoms
• C. $7.624\times {10}^5$ atoms
• D. $8.624\times {10}^5$ atoms

Answer 1

The correct option is A $1.686\times {10}^6$ atoms

$N_0=\frac{10.0}{3}\times 6.023\times {10}^{23}\times 8.0\times {10}^{-8}=1.606\times {10}^{17}$
$\lambda =\frac{0.693}{t_{1/2}}=\frac{0.693}{12.3}$
$N=N_0{e}^{-\lambda t}=1.606\times {10}^{17}{e}^{-\frac{0.693}{12.3}\times 40}=1.686\times {10}^{6}atoms$
Hence, $1.686\times {10}^6$ tritium atoms would 10.0g of such a sample contains 40 year after the original sample is collected.