Question

The initial mass of a radioactive isotope in a sample was $48$g. The half life of the isotope is $4$ days. The mass of isotope had decayed after $8$ days is $12$g.

• A. True
• B. False

Answer 1

The correct option is A True

Given,

Initial mass = 48 g

Half-life= 4 days

Time period = 8 days

Final mass = 12 g

We have the equation for half-life

$N=N_0(\frac{1}{2}{)}^{T/t_{1/2}}$

Where,

$N$ is the final mass

$N_0$ is the initial mass

$T$ is the time period

$t_{1/2}$ is the half-life

Now substituting the values in the above equation to find out the final mass, then we get

$N=48\times (\frac{1}{2}{)}^{\frac{8}{4}}$

$N=48\times (\frac{1}{2}{)}^2$

$N=\frac{48}{4}=12g$

So the final mass of the radioactive isotope is 12 g.