Question

A 3.289 g sample of technetium-95 is sealed in a container. After 44.2 hours, the amount of technetium-95 remaining is 0.709 g.

(a) Calculate the rate constant k for 95Tc.

                   1/h

(b) Calculate the half-life t1/2 for 95Tc.

                    h

Answer 1

The half life of the sample can be calculated using the formula

Nt = No (1/2)^{t / t 0.5}

where Nt is the amount of sample left after time t

No is the initial amount of sample

t is the amount of time lapsed

t 0.5 is the half life period of the sample

So putting all the values , we get ,

0.709 = 3.289 (1/2)^{44.2 / t 0.5}

t 0.5 = 19.96 hours

Since the radioactive decay are first order reactions

rate constant is given as

k = 0.693 / t 0.5

k = 0.693 / 19.96

k = 0.0347