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

Step-by-step explanation:

Given

half life
`(t_{(1)/(2))=4.5` billion year

10 % to decay i.e. 90 % remaining

And
`\ln ((C)/(C_0))=-kt`

where k= constant

t=time

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

so
`(C)/(C_0)=0.9`

`\ln (0.9)=-(\ln (2))/(4.5)* t`

t=0.684 billion year

(b)
`C_0=1.5* 10^(18)`

t=13.8 billion year

`\ln ((C)/(C_0))=-0.15403* 13.8`

`\ln ((C)/(C_0))=-2.125`

`C=C_0e^(-2.125)`

`C=1.5* 10^(18)* 0.1194=0.179* 10^(18)` atoms