Question

A sample of $0.42 \,mg \,{ }^{233} UF _{6}$ shows an activity of $9.88 \times 10^{4}$ count per second. Its $t_{1 / 2}$ is

• A. $5.13 \times 10^{12} yr$
• B. $1.628 \times 10^{5} yr$
• C. $2.94 \times 10^{-9} yr$
• D. $2.35 \times 10^{8} yr$

Answer 1

The Correct Option is B

Molecular mass of $U F_{6}=233+19 \times 6=347$ $\frac{d N}{d t} =k N $ $9.88 \times 10^{4} =k \times \frac{0.42 \times 10^{-3} \times 6.023 \times 10^{23}}{347}$ $\therefore k =1.35 \times 10^{-13}$ $k =\frac{0.693}{t_{1 / 2}}$ [$\because$ Radioactive changes follow Ist order kinetics.] or $ t_{1 / 2} =\frac{0.693}{1.35 \times 10^{-13}} s $ $=5.13 \times 10^{12} s $ $=1.628 \times 10^{5} \,yr .$