Answer:
Explanation:
Given
half life [tex](t_{\frac{1}{2})=4.5[/tex] billion year
10 % to decay i.e. 90 % remaining
And [tex]\ln (\frac{C}{C_0})=-kt[/tex]
where k= constant
t=time
and [tex]k=\frac{\ln (2)}{t_{\frac{1}{2}}}=\frac{\ln (2)}{4.5}[/tex]
so [tex]\frac{C}{C_0}=0.9[/tex]
[tex]\ln (0.9)=-\frac{\ln (2)}{4.5}\times t[/tex]
t=0.684 billion year
(b)[tex]C_0=1.5\times 10^{18}[/tex]
t=13.8 billion year
[tex]\ln (\frac{C}{C_0})=-0.15403\times 13.8[/tex]
[tex]\ln (\frac{C}{C_0})=-2.125[/tex]
[tex]C=C_0e^{-2.125}[/tex]
[tex]C=1.5\times 10^{18}\times 0.1194=0.179\times 10^{18}[/tex] atoms
