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 ___________.
Answer (integer)
25
Solution
<p>${N_1} = {{\left( {{{{{10}^{ - 2}}} \over 1}} \right)} \over {{2^4}}}$</p>
<p>${N_2} = {{\left( {{{{{10}^{ - 2}}} \over 2}} \right)} \over {{2^2}}}$</p>
<p>$\Rightarrow {{{N_1}} \over {{N_2}}} = {1 \over 2}$</p>
<p>$\therefore$ Mass ratio of A and B,</p>
<p>$${{{m_1}} \over {{m_2}}} = {{{N_1}} \over {{N_2}}} \times \left( {{{{M_1}} \over {{M_2}}}} \right)$$</p>
<p>$= {1 \over 2} \times \left( {{1 \over 2}} \right)$</p>
<p>$= {1 \over 4}$</p>
<p>$= {{25} \over {100}}$</p>
<p>$\therefore$ $x = 25$</p>
About this question
Subject: Physics · Chapter: Atoms and Nuclei · Topic: Bohr's Model of Hydrogen Atom
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