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

the correct answer would be b. amelia, because the particals of gas move really fast (charged particals) and gas also has a lot of room (particals move independently) so the only answer that has both of those is amelia's.