Question

A 96gram of sample of radioactive nuclide is placed in a container after 12min only 6gm of sample is undecayed .what is the half life of radioactive nuclide a)8hr b) 6hr c) 3hr?

Answer 1

See the explanation below.

Explanation:

Initial mass of nuclide is `m_0=96g`

Final mass of nuclide is `m_(12)=6g`

The time is `t=12mn`

The equation for the radioactive decay is

`m_(t)=m_0e^(-lambdat)`

Where `lambda` is the radioactive constant

Therefore,

`6=96*e^(-12lambda)`

`e^(12lambda)=96/6=16`

`12lambda=ln16=4ln2`

`lambda=1/3ln2`

But,

`lambda=ln2/t_(1/2)`

Therefore,

`t_(1/2)=ln2/lambda=ln2/(1/3ln2)=3mn`

The half life is `=3mn` and this does not fit the options given.