A certain nuclide has a half life of 30 minutes. If the sample containing `26xx10^(10)` atoms us allowed ti decay for `90` minutes, how many atoms will remain ?

Options

A. `2 xx 10^(10)` atoms
B. `4.5 xx 10^(9)` atoms
C. `7.5 xx 10^(9)` atoms
D. `1.5 xx 10^(9)` atoms

Answer

C

Explanation

No. of half left `=(90)/(30)=3`
No. of atoms left `=[(1)/(2)]^(n) xx` no. of atoms originally present
`=[(1)/(2)]^(3) xx 6xx10^(10)=(1)/(8)xx6xx10^(10)`
`=7.5xx10^(9)` atoms