A medical technician is working with the four samples of radionuclides listed in

Question

A medical technician is working with the four samples of radionuclides listed in the table below. Initially, each sample contains 17.00 mol of the radionuclide. First, order the samples by decreasing initial radioactivity. Then calculate how long it will take for the amount of radionuclide in each sample to decrease to 1/4 of the initial amount radionuclide time for amount of radionuclide to decrease to 1/4 of initial amount initial .radioactivity sample symbol half-life days days [] years A 26Fe 45 days (choose one) . Ru 241 95 osAm 432 years(choose one) 213 83 Bi 4 minutes (choose one) minutes

Explanation / Answer

The radioactive decay follows first order kinetics.

The rate law is

rate = k [Reactant}

= k x N t where Nt is the number of moles/atoms of nucleide at time t

The rate of disintegration(reaction) is called the activity of the nucleide

Thus activity A = rate = k x N

For first order reactions

rate constant k = 0.693/ half life

a) initial radioactivity

initial A = rate constant x initial concentration

Sample A  

initial activity A = (0.693/45)day-1 x17 x10-6 mol

= 2.618x10-7mol/day

Sample B

Initial acitivty A = (0.693/39)day-1 x17 x10-6 mol

=3.020x 10-7 mol/day

Sample C

Inital acitity A =(0.693/432)yr-1 x17 x10-6 mol

= 2.727x10-8 mol/yr

Sample D

Initial activity A = (0.693/45)min-1 x17 x10-6 mol

= 2.618x10-7 mol/min

b) time to become 1/4 of initial amount

For first order reactions half life is independent of starting material.

That is the time taken for a fixd fraction(say 50%) of reaction is same irrespective of the amount.

Thus from 100 to 50 it takes half life and from 50 to 25 also it takes another half life.

Thus the time taken for 3/4 disintegration(1/4 remaining) is always two half lifes for radioactive disnintegration.

Sample A time = 2 x 45 = 90days

sample B time = 2 x 39 = 78days

sample C time = 2 x 432 = 864 years

sample D time = 2 x 45 = 90min

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