10 g of a radioactive isotope is reduced to 1.25 g in 12 years. Therefore half-life period of the isotope is

Options

A. 24 years
B. 4 years
C. 3 years
D. 8 years

Answer

B

Explanation

(b) : `[A]=([A]_(0))/(2^(n)):.1.25=(10)/(2^(n))" or "2^(n)=(10)/(1.25)=8=2^(3):.n=3`
i.e., 3 half lives = 12 yrs. `" or "t_(1//2)=4" yr"`
Alternatively, `10goverset(t_(1//2))to5goverset(t_(1//2))to2.5goverset(t_(1//2))to1.25g`
`3xxt_(1//2)=12" yr or "t_(1//2)=4" yr".`