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?

= 72900 years

Explanation:

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.

The number of years that will pass before 8 kg of the isotope of plutonium-239 will reduce to 1 kg is  72900 years.

We'll begin by calculating the number of half-lives that has elapsed. This can be obtained as follow:

Original amount (N₀) = 8 kg

Amount remaining (N) = 1 kg

N × 2ⁿ = N₀

1 × 2ⁿ = 8

2ⁿ = 8

2ⁿ = 2³

Thus, 3 half-lives has elapsed

Finally, we shall determine the time taken for the isotope to reduce to 1 Kg. This can be obtained as follow;

Number of half-lives (n) = 3

Half-life (t½) = 24300 years

t = n × t½

t = 3 × 24300

Therefore, it will take 72900 years for 8 kg of the isotope of plutonium-239 to reduce to 1 kg.

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