Question

The half-life for the radioactive decay of U-238 is 4.5 billion years and is independent of initial concentration. How long will it take for 10% of the U-238 atoms in a sample of U-238 to decay? If a sample of U-238 initially contained 1.5×10181.5×1018 atoms when the universe was formed 13.8 billion years ago, how many U-238 atoms does it contain today?

Answer 1

Answer:

Explanation:

Given

half life $(t_{\frac{1}{2})=4.5$ billion year

10 % to decay i.e. 90 % remaining

And $\ln (\frac{C}{C_0})=-kt$

where k= constant

t=time

and $k=\frac{\ln (2)}{t_{\frac{1}{2}}}=\frac{\ln (2)}{4.5}$

so $\frac{C}{C_0}=0.9$

$\ln (0.9)=-\frac{\ln (2)}{4.5}\times t$

t=0.684 billion year

(b)$C_0=1.5\times 10^{18}$

t=13.8 billion year

$\ln (\frac{C}{C_0})=-0.15403\times 13.8$

$\ln (\frac{C}{C_0})=-2.125$

$C=C_0e^{-2.125}$

$C=1.5\times 10^{18}\times 0.1194=0.179\times 10^{18}$ atoms