Question

$\,^{221}_{87}$Ra undergoes radiorctive decay with a half life of 4 days. The probability that a Ra nucleus will disintegrate in 8 days is

• A. 1
• B. $\frac{1}{2}$
• C. $\frac{1}{4}$
• D. $\frac{3}{4}$

Answer 1

Answer: (D)

$\frac{3}{4}$

Answer 2

$n = \frac{t}{t_{1/2}} = \frac{8}{4} = 2 ; N_o = 2^n N$ $\frac{N_o}{N} = 2^2 = 4$ Remaining atoms = N = $\frac{N_o}{4}$ Dacayed atoms = $N_o - N = N_o - \frac{N_o}{4} = \frac{3N_o}{4}$ $\therefore$ Probability of decay = $\frac{N_o - N}{N_o} = \frac{3}{4}$