`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. a. 8 hr
B. b. 24 hr
C. c. 6 hr
D. d. 4 hr

Answer

a. 8 hr

Explanation

`N = ((1)/(2))^(n) N_(0) implies 125 mg = ((1)/(2))^(n) 1000`
`:. (125)/(1000) = ((1)/(2))^(n) implies ((1)/(2))^(3) = ((1)/(2))^(n) implies n = 3`
Using `T = nt_(1//2), t_(1//2) = (24)/(3) = 89 hr`