`1.0 g` of a radioactive isotope left `125 mg` after 24 hr. The half-life period of the isotope is
a. 8 hr b. 24 hr c. 6 hr d. 4 hr

Options

A. 8 hours
B. 24 hours
C. 6 hours
D. 4 hours

Answer

A

Explanation

`N = [(1)/(2)]^(n) xx N_(0) = 125mg = ((1)/(2))^(n) xx 1000 mg`
`((1)/(2))^(n) = (125)/(1000) = (1)/(8)`
`((1)/(2))^(n) = ((1)/(2))^(3), n = 3`, so number, of `t_(1//2) = 3`
Total time = 24 hours, Half-life time = `(24)/(3)` = 8 hours.