Question

A radioactive sample has $5000$ disintegration per minute initially and $1250$ disintegration per minute after $5$ seconds. Then the decay constant is

• A. $0.4ln2$
• B. $0.2ln2$
• C. $0.1ln2$
• D. $0.8ln2$

Answer 1

Answer: (A)

$0.4ln2$

Using formulae, $N=N_o{e}^{-\lambda t}$

$\Rightarrow 1250$ $=5000e^{-\lambda 5}$

$\Rightarrow ln\left(\frac{1}{4}\right)=-\lambda 5\Rightarrow 2ln2=5\lambda$

$\Rightarrow \lambda =0.4ln2.$