Question

You have 100 g of radioactive plutonium-239 with a half-life of 24,000 years. How much will remain after
a) 12,000 years
b) 24,000 years and
c) 96,000 years

Answer 1

Radioactive decay also known as nuclear decay or nuclear disintegration and can be defined as the process by which an unstable atomic nucleus loses energy in the form of radiations. Molecule which contains an unstable nucleus is known as radioactive.

Complete answer:
Plutonium-239 has a half-life of 24,000 years where half-life can be defined as the number of years it takes for a radioactive substance to decay half of its original mass or weight or in simple manner we can describe it that time period by which mass remains half.
Now half-life of plutonium-239 is 24,000 years which means that if 100 g of plutonium-239 is there then this means that it remains exactly half within these years i.e. 50 g.
Similarly we can calculate it for 12000 years, it needs only $\dfrac{1}{2}$ of its half-life which suggests that it has decayed only $\dfrac{1}{2}\times \dfrac{1}{2}=\dfrac{1}{4}$of its weight, so $1-\dfrac{1}{4}=\dfrac{3}{4}$still remains.
Therefore it remains $\dfrac{3}{4}\times 100=75g$after 12000 years.
96000 years will be equal to $\dfrac{96000}{24000}=4$half-life then we know that
For zero half-life period we have 100 g
For one 50 g
For two 25 g
For three 12.5 g
For four 6.25 g
Hence for 100 g of radioactive plutonium-239 with a half-life of 24,000 years. It will remain after
a) 12,000 years = 75 g
b) 24,000 years = 50 g and
c) 96,000 years = 6.25 g

Note:
Plutonium-239 is basically an isotope of plutonium. It is the primary fissile isotope which is used for the production of nuclear weapons rather than this uranium-235 has also been used. Plutonium-239 is also one of the three main isotopes used as fuel in thermal spectrum nuclear reactors along with uranium-235 and uranium-233.