i. What do you understand by the term rate of decay and give its mathematical expression.

i. Rate of decay of a radioelement denotes the number of nuclei of its atoms which decay in unit time. It is also called activity of radioelement.

Rate of decay at any time t can be expressed as follows :

Rate of decay (activity) = \(-\frac{dN}{dt}\) 

Where, 

dN is the number of nuclei that decay with in time interval dt.

ii. Minus sign in the expression indicates that the number of nuclei decreases with time. 

Therefore,

dN is a negative quantity. 

But, 

The rate of decay is a positive quantity. 

The negative sign is introduced in the rate expression to make the rate positive.