Question

The Environmental Protection Agency and health officials nationwide are concerned about the levels of radon gas in homes. The half-life of the radon-222 isotope is 3.8 days. If a sample of gas taken from a basement contains 2.1 µg of radon-222, how much radon will remain in the sample after 4.94 days? Answer in units of µg.

Answer 1

Answer: The amount left after 4.94 days is
`0.875\mu g`

Step-by-step explanation:

Expression for rate law for first order kinetics is given by:

`t=(2.303)/(k)\log(a)/(a-x)`

where,

k = rate constant

t = age of sample

a = let initial amount of the reactant

a - x = amount left after decay process

a) for completion of half life:

Half life is the amount of time taken by a radioactive material to decay to half of its original value.

`t_{(1)/(2)}=(0.693)/(k)`

`k=(0.693)/(3.8)=0.18days^(-1)`

b) to calculate amount left after 4.94 days

`t=(2.303)/(0.18)\log(2.1\mu g)/(a-x)`

`4.94=(2.303)/(0.18)\log(2.1\mu g)/(a-x)`

`\log(2.1\mu g)/(a-x)=0.39`

`(2.1\mu g)/(a-x)=2.4`

`{a-x}=0.875\mu g`

The amount left after 4.94 days is
`0.875\mu g`