Question

The half-life of the radioactive isotope polonium-218 is 3.05 minutes.

How long will it take for the activity of a sample of polonium-218 to decrease from 2.81E4 Ci to 3.52E3 Ci?

Answer 1

Answer: It will take 9.13 minutes for the sample.

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 = initial amount of the reactant =
`2.81* 10^4`

a - x = amount left after decay process =
`3.52* 10^3`

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)/(3.05min)=0.227min^(-1)`

b) for activity to decrease from 2.81E4 Ci to 3.52E3 Ci:

`t=(2.303)/(0.227)\log(2.81* 10^4)/(3.52* 10^3)`

`t=9.13min`

Thus it will take 9.13 minutes for the sample.

`t_(99.9)=40min`

The time after which 99.9% reactions gets completed is 40 minutes