Question

Two isotopes P and Q of atomic weight 10 and 20, respectively are mixed in equal amount by weight. After 20 days their weight ratio is found to be 1 : 4. Isotope P has a half-life of 10 days. The half-life of isotope Q is

• A. zero
• B. 20 days
• C. infinite
• D. 5 days

Answer 1

Answer: (D)

Let Wg of each be taken initid modes of P

$\begin{array}{c}=\frac{W}{10}\\ \varnothing =\frac{W}{20}\\ FindP=\frac{W_1}{5\times 10}\\ \varnothing =\frac{4W_1}{20\times 5}\\ \therefore for{P}_1\frac{W\times 5\times 10}{10W_1}={\ell }^{\times P\times 20}\to \left(i\right)\\ for\varnothing {1pt}_1\frac{W\times 20\times 5}{20\times W_1\times 4}={\ell }^{\lambda \varnothing \times 20}\to \left(ii\right)\\ from\left(1\right)\&\left(2\right)\\ 4{\ell }^{\left(\lambda P-\lambda \varnothing \right)\times 20}\\ 20\left(\lambda P-\lambda \varnothing \right)=\log e^4\\ 20\left(\frac{0.693}{t_{\frac{1}{2}}}-\frac{0.693}{10}\right)=\log e^4\\ t_{\frac{1}{2}}=5\end{array}$