Question

If 14 g of a radioactive substance are present initially and 3 years later only 7 g remain, how much of the substance will be present after 4 yr?

Answer 1

5.56 g

Explanation:

We are given;

• Original mass of radioactive isotope is 14 g
• Mass remaining after 3 years is 7 g

• But, we know that half life is the time taken by a radioactive isotope to decay to half of its original mass.

• Therefore, Half life of the radioactive substance is 3 years.

We need to determine the mass that will be present after 4 years.

• Number of half lives = 4 years ÷ 3 years

= 4/3

Using the formula;

• Remaining mass = Original mass × 0.5^n

Therefore;

Remaining mass = 14 g × 0.5^4/3

= 5.56 g

Thus, the remaining mass after 4 years will be 5.56 g