Question

A freshly prepared radioactive source of half-life 2h emits radiation of intensity which is 64 times the permissible safe level.

Answer 1

Let the permissible radiation level be K. Current emission is 64K

In 2 years, it will emit 32K

In 4 years, it will emit 16K

in 6 years, it emits 8K

and so on

In 12 years, the sample will emit radiation at level K, which is suitable for work

Answer 2

The minimum time after which it is possible to work safely with the source is 12h.

Half life of the radioactive source = 2h

Intensity of the safe level = 64 times

Thus,

First order decay -

N ( t ) = Ne `-λt

t1/2 = ln2/ λ = 2hr

1/64 = e`-2t

t = 12h

Thus, the minimum time after which it is possible to work safely with the source is 12h.