Question

If 0.04625 mg. of Uranium-235 remains after 2.8 x 10^9 years, what was
the original mass of the sample of Uranium-235? The half-life of Uranium-235 is 7.0 x 10^8 years.

Answer 1

Answer: The original mass of the sample of Uranium-235 is 0.7308 mg

Explanation:

Expression for rate law for first order kinetics is given by:

$t=\frac{2.303}{k}\log\frac{a}{a-x}$

where,

k = rate constant

t = age of sample

a = let initial amount of the reactant

a - x = amount left after decay process  

a) for calculating rate constant

$t_{\frac{1}{2}}=\frac{0.693}{k}$

$k=\frac{0.693}{7.0\times 10^8years}=0.099\times 10^{-8}years^{-1}$

b) for time of $2.8\times 10^9$ years

$2.8\times 10^9=\frac{2.303}{0.099\times 10^{-8}}\log\frac{a}{0.04625}$

$\log\frac{a}{0.04625}=1.2$

$\frac{a}{0.04625}=15.8$

$a=0.7308mg$

The original mass of the sample of Uranium-235 is 0.7308 mg