The half life of radon-222 is 3.8 days. how much of a 100 gram sample is left after 15.2 days ?

6.3g of the 100g sample will be left after 15.2years

Explanation:

Half life is defined as the time taken by a radioactive substance to decay or reduce to half if its original value.

Mathematically, t1/2 = 0.693/¶ where ¶ is the decay constant.

Firstly, we need to get the decay constant using the formula for half life.

Given half life of radon (t1/2) = 3.8days

3.8 = 0.693/¶

¶ = 0.693/3.8

¶ = 0.182

If the initial value (No) if the substance is 100, the final sample (N) after 15.2years of decay can be gotten using the formula

N= Noe^-¶t where

N is the final sample after decay

No is the initial value of the sample

¶ is the decay constant

t is the time taken NY the object to decay

Given No = 100

¶ = 0.182

t = 15.2years

Substituting in the formula to get N we have;

N = 100e^-0.182(15.2)

N = 100e^-2.7664

N = 100×0.063

N = 6.3g

This shows that the initial value of radon would have decay upto 6.3g after 15.3years