The spent fuel of a nuclear reactor contains plutonium-239, which has a half-life of 24,000 years. if 1 barrel containing 10 kg of plutonium-239 is sealed, how many years must pass until only 10 g of plutonium-239 is left? use y = y0 *e^ -(kt). (round your answer to the nearest integer.

This fuel will require 239230 years.

Explanation:

All the radioactive reactions follow first order kinetics.

The equation used to calculate rate constant from given half life for first order kinetics:

We are given:

Putting values in above equation, we get:

The equation used to calculate time period follows:

where,

= initial mass of isotope  = 10 kg = 10000 g     (Conversion factor: 1 kg = 1000 g)

N = mass of the parent isotope left after the time = 10 g

t = time = ? years

k = rate constant =

Putting values in above equation, we get:

Hence, this fuel will require 239230 years.