Question

After 24 hours, how many grams will be left of an 800 g sample of the imaginary radioactive isotope Sciencium that has a half life of 4 hours? Grams of Scienclum after 24 hours=_____.

Answer 1

Given data:

The mass of sample is m=800 g.

The halft life of sample is T=4 hrs.

The time at which mass is required is t=24 hr.

The formula to calculate the mass left in a radioactive decay is given by,

$m(t)=m(\frac{1}{2})^{\frac{t}{T}}$

Here, m(t) is the mass at t=24 hrs.

Substitute the given values in above equation,

$\begin{gathered} m(24)=(800)(\frac{1}{2})^{\frac{24}{4}} \\ m(24)=12.5\text{ gram} \end{gathered}$

Thus, the mass of radioactive isotoper after 24 hrs is 12.5 gram.