Question 398: Atoms & Nuclei

Question

A sample contains 10$$-$$2 kg each of two substances A and B with half lives 4 s and 8 s respectively. The ratio of their atomic weights is 1 : 2. The ratio of the amounts of A and B after 16 s is $${x \over {100}}$$. The value of x is ___________.

Accepted Answer

$${N_1} = {{\left( {{{{{10}^{ - 2}}} \over 1}} ight)} \over {{2^4}}}$$
$${N_2} = {{\left( {{{{{10}^{ - 2}}} \over 2}} ight)} \over {{2^2}}}$$
$$ \Rightarrow {{{N_1}} \over {{N_2}}} = {1 \over 2}$$
$$	herefore$$ Mass ratio of A and B,
$${{{m_1}} \over {{m_2}}} = {{{N_1}} \over {{N_2}}} 	imes \left( {{{{M_1}} \over {{M_2}}}} ight)$$
$$ = {1 \over 2} 	imes \left( {{1 \over 2}} ight)$$
$$ = {1 \over 4}$$
$$ = {{25} \over {100}}$$
$$	herefore$$ $$x = 25$$

Atoms & Nuclei

A sample contains 10$-2 kg each of two substances A and B with half lives 4 s and 8 s respectively. The ratio of their atomic weights is 1 : 2. The ratio of the amounts of A and B after 16 s is {x \over {100}}$. The value of x is ___________.

Choose the correct answer: