Question

A radioactive sample has an initial activity of $28dpm$, half hour later the activity is $14dpm$. How many atoms of the radioactive nuclide were there originally?
$(\ln 2=0.7)$

• A. $12$
• B. $200$
• C. $600$
• D. $300$

Answer 1

The correct option is A $12$

The correct option is A

$\lambda$=$\frac{2.303}{t}log\frac{N_o}{N}$

$\frac{N_o}{N}=\frac{28}{14}=2,t=\frac{1}{2}hours=30$ min

$\lambda =\frac{2.303}{30min}=log2$

$\frac{2.303\times 0.3010}{30}mi{n}^{-1}$

$0.0231min-1$

Rate=$\lambda N_o$

$28=0.0231\times N_o$

$N_o=\frac{28}{0.0231}=1212$