Nuclei

Given that the half-life of a radioactive substance is So, .
For decay, we have of the substance left, hence

where initial undecayed substance and is the time taken for decay.
For decay, we have of the substance left, hence

Dividing E (i) and E (ii), we get


(taking log on both sides)

In the reaction, we have to conserve the mass number and the atomic number. thus, we have

So,
Hence, and
Hence,
So, we have

to So, we can say that

Given, days
Number of active nuclei remaining after time ,

After days.


After days,

Number of nuclei that will decay on the rd day,

In the term, fraction is