Question

A sample of radioactive substance shows an intensity of 2.3 mCi at a time t and an intensity of 1.62 mCi 600 s later, what is the half life and average life of radioactive material?

• A. 1186.15 s, 1812.33 s
• B. 1236.15 s, 1712.33 s
• C. 1566.15 s, 1712.33 s
• D. 1186.15 s, 1712.33 s

Answer 1

Answer: (D)

1186.15 s, 1712.33 s

$r_1=2.3\times {10}^{-3}$ curie
$r_2=1.62\times {10}^{-3}$ curie, when t = 600 s
$\therefore \frac{r_1}{r_2}=\frac{2.3\times {10}^{-3}}{1.62\times {10}^{-3}}=\frac{N_1}{N_2}$
$(\therefore r\propto$ Number of atoms)
$K=\frac{2.303}{t}log\frac{N_1}{N_2}$
$=\frac{2.303}{600}log\frac{2.3}{1.62}$
$=5.84\times {10}^{-1}{s}^{-1}$
$\therefore t_{1/2}=\frac{0.693}{K}=\frac{0.693}{5.84\times {10}^{-4}}=1186.15s$
T(average life) $=\frac{1}{K}=\frac{1}{5.84\times {10}^{-4}}$
= 1712.33 s
or,
$T=1.44\times t_{1/2}=1.44\times 1186.15$
= 1712.33 s