If you have 100 g of radioactive isotope with a half-life of 10 years:
how much of the isotope will you have left after 10 years?
how much of the isotope will you have left after 20 years?
how many half lives will occur in 40 years?

#1. 50 g

#2. 25 g

#3. 4 half lives

We are given;

We need to answer the questions:

#a. Mass remaining after 10 years

Using the formula;

Remaining mass = Original mass × 0.5^n , where n is the number of lives.

In this case, since the half life is 10 years then n is 1

Therefore;

Remaining mass = 100 g × 0.5^1

                            = 50 g

Therefore, 50 g of the isotope will remain after 10 years

#b. Mass of the isotope that will remain after 20 years

Remember the formula;

Remaining mass = Original mass × 0.5^n

n = Time ÷ half life

n = 20 years ÷ 10 years

   = 2

Therefore;

Remaining mass = 100 g × 0.5^2

                           = 25 g

Thus, 25 g of the isotope will be left after 20 years

#3. Number of half lives in 40 years

1 half life = 10 years

But; n = time ÷ half life

          = 40 years ÷ 10 years

          = 4

Thus, the number of half lives in 40 years is 4.