A radioactive nucleus with a half life , decays into a nucleus . At , there is no nucleus . At some time , the ratio of the number of to that of is . Then, is given by:
Step 1: Given data
Half life
At , there is no nucleus
Step 2: Find
Let be decay constant.
Since the radioactive nucleus has half life , the decay constant become
At , there is no nucleus . So,
Let initial number of atomic nuclei
The number of
The number of
At some time
The number of
The number of
The ratio of the number of to that of is
Put value of , we get,
Hence, option B is correct.