Question
Obtain the relation between the decay constant and half-life of a radioactive sample.
The half-life of a certain radioactive material against 
decay is 100 days. After how much time, will the undecayed fraction of the material be 6.25%?
Solution
In a radioactive sample, number of atoms at any instant is given by, 
Now, when t = T, where T is the half-life of the sample.
This implies, half-life of a radioactive substance is inversely proportional to decay constant.
Numerical:
We have,
Number of undecayed nuclei left = 6.25 % = 6.25/ 100 = 1/16
Let, t be the required time after which the undecayed fraction of the material will be 6.25%.
