Question

The half-life of ${}^{238}$U for $\alpha$- decay is $4.5\times {10}^9$ years. The number of disintegration per second occur in 1g of ${}^{238}$U is
(Avogadro's number=6.023 10${}^{23}mo{l}^{-1}$)

• A. $1.532\times 10$${}^4{s}^{-1}$
• B. $1.325\times 10$${}^4{s}^{-1}$
• C. $1.412\times 10$${}^4{s}^{-1}$
• D. $1.235\times 10$${}^4{s}^{-1}$

Answer 1

Answer: (D)

$1.235\times 10$${}^4{s}^{-1}$

$t_{1/2}=4.5\times {10}^{9}years$

$=4.5\times {10}^9\times 3.16\times {10}^{7}s$

$=1.42\times {10}^{17}s$

One mol of any isotope contains Avogadros no. of atoms and so 1g of U contains

$=\frac{1}{238}mol\times 6.025\times {10}^{23}atoms/mol$

$=25.3\times {10}^{20}atoms$

The decay rate R is:

$R=N$

$=\frac{0.693}{1.42\times {10}^{17}}\times 25.3\times {10}^{20}$

$=1.23\times {10}^4{s}^{-1}$