Question

After 24 hours only 0.125gm out of the initial quantity of 1gm of a radioactive isotopes remain behind. Whar is its half life period

Answer 1

The decay proceeds like this,
Initially 1g
After 1 half life, it is 0.5g
After 2 half life, it is 0.25g
After 3 half life, it is 0.125g
So,
Half life of the given sample
=Total time taken/No. of half lives
=24/3
=8 hours

Answer 2

Initial concentration (a) = 1 g

Final concentration (x) = 0.125 g

Time taken (t) = 24 hours

∴k = 2.303/t {log[(a)/(a-x)]}

    = 2.303/24 [log(1)-log(0.125)]

    = 2.303/24 (0.9031)

    = 0.085 hr ⁻¹

∴Half life = 0.693/k

               = 0.693/0.085

               = 8.15 hrs