Question

Radioactive equilibrium is established in a uranium mineral between radium and uranium atom in the ratio 1 : 28. If half-life period of radium is 1620 years, calculate the disintegration constant of uranium.

• A. $4.844\times {10}^{-13}{s}^{-1}$
• B. $5.844\times {10}^{-16}{s}^{-1}$
• C. $7.844\times {10}^{-15}{s}^{-1}$
• D. None of these

Answer 1

The correct option is A $4.844\times {10}^{-13}{s}^{-1}$

$N_1{\lambda }_1=N_2{\lambda }_2$
radium uranium

$\frac{{\lambda }_1}{{\lambda }_2}=\frac{N_1}{N_2}=\frac{28}{1}$

$\frac{{\left(\frac{0.693}{t_{50}}\right)}_1}{{\left(\frac{0.693}{t_{50}}\right)}_2}=\frac{(t_{50}{)}_2}{(t_{50}{)}_1}=\frac{28}{1}$

$(t_{50}{)}_2=1620\times 28$ years $=1.43047\times {10}^{12}s$

$\therefore {\lambda }_2=\frac{0.693}{t_{50}}=4.844\times {10}^{-13}{s}^{-1}$