Radon-222 ( 222/86 rn) is a radioactive gas with a half-life of 3.82 days. a gas sample contains 4.1 e 8 radon atoms initially.

a) determine how many radon atoms will remain after 12 days.

b) determine how many radon nuclei will have decayed by this time.

Answer :

(a) The number of radon atoms will remain after 12 days is,

(b) The number of radon nuclei have decayed by this time will be,

Explanation :

For part (a) :

Half-life = 3.82 days

First we have to calculate the rate constant, we use the formula :

Now we have to calculate the number of radon atoms will remain after 12 days.

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

where,

k = rate constant  =

t = time passed by the sample  = 12 days

a = initially number of radon atoms  =

a - x = number of radon atoms left = ?

Now put all the given values in above equation, we get

Thus, the number of radon atoms will remain after 12 days is,

For part (b) :

Now we have to calculate the number of radon nuclei will have decayed by this time.

The number of radon nuclei have decayed = Initial number of radon atoms - Number of radon atoms left

The number of radon nuclei have decayed =

The number of radon nuclei have decayed =

Thus, the number of radon nuclei have decayed by this time will be,

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