The half life period of a radioactive substance is 10 hours. How much will be left after 4 hours in 1g atom sample ?

Options

A. `45.6 xx 10^(23)` atom
B. `4.56 xx 10^(23)` atom
C. `4.56 xx 10^(21)` atom
D. `4.56 xx 10^(20)` atom

Answer

B

Explanation

`[N]_(0)="1 atom" = 6.02 xx 10^(23)`
`[N]=?`
`t_(1//2)=10` hour
`:. K = (0.693)/(10 hr) = 0.0693 hr^(-1)`
`t = (2.303)/(k) "log"([N]_(0))/([N])`
`t=(2.303)/(0.693 "hr"^(-1))"log"([N]_(0))/([N])`
`4hr=(2.303)/(0.693"hr"^(-1))"log"([N]_(0))/([N])`
`"log"([N]_(0))/([N])=(0.693xx4)/(2.303)=0.12`
`([N]_(0))/([N])="antilog"0.12 =1.318`
`[N]=([N]_(0))/(1.318)=(6.022xx10^(23))/(1.318)=4.56xx10^(23)`.