Question

The half-life of a radioisotope is 4 hours. If the initial mass of the isotope was $200$ g, the mass remaining after $24$ hours undecayed is:

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

Answer 1

Answer: (C)

$3.125g$

Let the undecayed mass be $x$,

$t_{1/2}=\frac{ln2}{\lambda }$ where $\lambda$ is decay constant.

$\lambda =\frac{ln2}{4}hou{r}^{-1}$

Initial mass $=200g$

Using first order kinetics equation at $t=24hours$

$\frac{ln2}{4}\times 24=ln\left(\frac{200}{x}\right)$

$\frac{200}{x}=64$

$x=\frac{200}{64}=3.125g$