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

Engineering

Physics

SI Units

Calculus

Radioactivity New

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

zero

5 days

20 days

infinite

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Let Wg of each be taken initid modes of P

\frac{W}{10}

Ø =

\frac{W}{20}

Find p =

\frac{W_{1}}{5 \times 10}

Ø =

\frac{4 W_{1}}{20 \times 5}

for P₁ =

\frac{W \times 5 \times 10}{10 W_{1}}

= l^×p×20 → (i)

for Ø ¹pt₁ =

\frac{W \times 20 \times 5}{20 W_{1} \times 4}

= l^λØ×20 → (ii)

From (1) , (2)

4l^{(λP – λØ)×20}

20(λP – λØ) = loge⁴

(\frac{0.693}{t_{\frac{1}{2}}^{2}} - \frac{0.693}{10}) = {loge}^{4}

\frac{1}{2}

= 5