Question

The half-life of plutonium-239 is 24300. If a nuclear bomb released 8kg of this isotope, how many years would pass before the amount is reduced to 1kg?

Answer 1

Answer:

= 72900 years

Explanation:

• The half-life is the time taken by a radioactive material to decay by half the original amount.
• The half-life of plutonium-239 is 24300 years which means it takes 24300 years to decay by half the original amount.

To calculate the time taken for a mass of 8 kg to decay to 1 kg we use;

New mass = Original mass x (1/2) ^n, where n is the number of half-lives

Therefore;

1 kg = 8 kg × (1/2)^n

1/8 = (1/2)^n

solving for n;

n =3

Therefore;

Time = 3 × 24300 years

          = 72900 years

It will, therefore, take 72900 years for 8 kg of plutonium-239 to decay to 1 kg.