Answer:
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
