Substance A has atomic mass number 16 and half-life of 1 day. Another substance B has atomic mass number 32 and half-life of day. [2023]

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Solution

Q.
Substance A has atomic mass number 16 and half-life of 1 day. Another substance B has atomic mass 1 number 32 and half-life of $\frac{1}{2}$ day. If both A and B simultaneously start undergo radioactivity at the same time with initial mass 320 g each, how many total atoms of A and B combined would be left after 2 days. [2023]

1 $3.38 \times 10^{24}$

2 $6.76 \times 10^{24}$

3 $6.76 \times 10^{23}$

4 $1.69 \times 10^{24}$

Ans.
(1)

${(N_{0})}_{A} = \frac{320}{16} = 20 moles$

${(N_{0})}_{B} = \frac{320}{32} = 10 moles$

$N_{A} = \frac{{(N_{0})}_{A}}{{(2)}^{2 / 1}} = \frac{20}{4} = 5$

$N_{B} = \frac{{(N_{0})}_{B}}{{(2)}^{2 / 5}} = \frac{10}{2^{4}} = 0.625$

$Total N = 5.625$

$Number of atoms = 5.625 \times 6.023 \times 10^{23} = 3.38 \times 10^{24}$

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