Question

The half life period of a radioactive isotope is 2hours. After 6hours what fraction of the initial quantity of the isotope will be left behind?

Answer 1

Now the half life of the isotope is given 2 hours. After 6 hours the no of half lives will be 3.

So the The amount of radioactive isotope remaining can be calculated as:

Nt = No x 1/2^n where, Nt is the amount of radio isotope remaining. No is the original amount of radio isotope.

N is the no of half lives.

Now let the original amount of isotope is one, then by using the formula we can calculate the remaining of isotope as:

Nt = 1x1/2^3

= 1x1/8

= 1/8

Answer 2

If initial quantity of a radioactive isotope is N₀, after n complete half lives, the quantity remaining will be $\frac{N_0}{2^n}$.

Half life = 2 hours
time = 6 hours
number of half lives = 6/2 = 3

So quantity of isotope left behind = $\frac{N_0}{2^3}= \frac{N_0}{8}$

So only $\frac{1}{8}$ of the initial quantity will remain after 6 hours.