Half life period of radioactive element is 20 days . What will be the remaining mass of 100 g of it after 60 days ? Answer is 12.5 gram. Please explain?

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Answer

Calculation of Radioactive Decay

Definition of Half-Life Period
The half-life period of a radioactive element is the time it takes for half of the original mass of the element to decay.

Calculation of Decay Constant
The decay constant is the fraction of the original mass that decays in one unit of time. It is calculated as:

λ = ln 2 / t1/2

where ln 2 is the natural logarithm of 2 and t1/2 is the half-life period.

In this case, the decay constant is:

λ = ln 2 / 20 = 0.034657

Calculation of Remaining Mass
The remaining mass of a radioactive element after a certain amount of time can be calculated using the following equation:

m = m0 * e^(-λt)

where m0 is the initial mass of the element, t is the time elapsed, and e is the mathematical constant approximately equal to 2.718.

In this case, we want to find the remaining mass of a 100 g sample after 60 days:

m = 100 * e^(-0.034657*60) = 12.5 g

Therefore, the remaining mass of the radioactive element after 60 days is 12.5 g.

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