Plutonium-239 has a half-life of 24,100 years. How long will it take a 1-kilogram sample to decay to 125 grams?

72,300 years are required to reduce Plutonium-239 from 1000 g to 125 g.

Explanation:

It is known that 1 kg of anything is equal to 1000 g of the same compound. Also the half life of any radioactive element meant decay of half of the weight of that element after the half life time.

As here the half life time of Plutonium-239 is said to be 24,100 years. This means after the first interval of 24,100 years, the plutonium-239 of 1000 g will reduce to 1000/2=500 g of plutonium. That means only 500 g of plutonium 239 will be present after the completion of first interval of 24,100 years.

Similarly, the second interval of 24,100 years will again reduce the mass from 500 g to 250 g. Then the third interval of 24,100 years will reduce the mass from 250 g to half of it i. e., 125 g of plutonium. Thus, as per the question, the time taken to reduce 1 kg of plutonium to 125 g of plutonium will require three intervals of half life time. Thus, the total time required to reduce the concentration from 1000 g to 125 g is No. of intervals * Half life time.

Total time required to reduce the weight from 1000 g to 125 g = No. of interval * Half life time

Total time = 3 * 24100 years = 72,300 years.

So 72,300 years are required to reduce Plutonium-239 from 1000 g to 125 g.