Question

The half-life of radio isotope is 4 hr. If initial mass of the isotope was 200 g, then mass remaining after 24 hr will be

• A. 1.042 g
• B. 2.084 g
• C. 3.125 g
• D. 4.167 g

Answer 1

Answer: (C)

3.125 g

A radioactive decay is a first order reaction.

The reaction constant for a first order reaction is, $\lambda =\frac{ln2}{\tau }$

where $\tau$ is the half life of the substance.

Amount of substrate remaining after time $t$ will be:

$N=N_0{e}^{-\lambda t}$

$=N_0{e}^{-\frac{ln2}{\tau }t}$

$=200\times e^{-\frac{ln2}{4}\times 24}g=3.125g$