Question

There were 5 kg of Pu-238 in the nuclear battery of the Voyager 2 when it was launched. Pu-238 has a half-life of 88 years. In how many years will there be 1.25 kg of Pu-238 left?

Answer 1

The half-life of Pu-238 is 88 years. To find the number of years it will take for there to be 1.25 kg of Pu-238 left, we set up an equation. By solving for the exponent, we can determine the number of half-lives that need to occur.

Step-by-step explanation:

The half-life of Pu-238 is 88 years. This means that every 88 years, half of the original amount of Pu-238 will decay. In this case, the original amount is 5 kg, and we want to know how many years it will take for there to be 1.25 kg left.

Since half of the original amount decays every 88 years, we can set up the equation:

1. 5 kg / (2x) = 1.25 kg

To solve for x, we need to find the exponent. Taking the logarithm of both sides, we get:

1. x = log2(5/1.25)

Using a calculator, we find that x ≈ 2.

Therefore, it will take approximately 2 times 88 years, or 176 years, for there to be 1.25 kg of Pu-238 left.