A certain radioactive element has a half-life of 20 years . If we have a block with 10 g of the element in it, after how

Options

A. 80 years
B. 40 years
C. 100 years
D. 60 years

Answer

B

Explanation

`T_(1//2)=20` years
`N_(0)=10g `
`N=2.5` g
`N=N_(0)e^(-lambdat)" "lambda=(0.693)/(T_(1//2))`
`implies e^(-lambdat)="In" ((N)/(N_(0)))`
`implies t=(1)/(lambda) " In " ((N_(0))/(N))=(T_(1//2))/(0.693)xx "In" ((N_(0))/(N))`
`=(20)/(0.693)xx "In" ((10)/(2.5))=40` years