a) Deduce the expression, N = N₀ e^−λt, for the law of radioactive decay.

(b) (i) Write symbolically the process expressing the β⁺ decay of  . Also write the basic nuclear process underlying this decay.

(ii) Is the nucleus formed in the decay of the nucleus  , an isotope or isobar?

As per the law of radioactive decay, we have

where,

N = Number of nuclei in the sample

ΔN = Amount of nuclei undergoing decay

Δt = Time taken for decay 

(b)

(i) The β⁺ decay for  is given below:

A proton is converted into neutron if, the unstable nucleus has excess protons than required for stability.

In the process, a positron e⁺ (or a β⁺) and a neutrino ν are created and emitted from the nucleus.

p → n + β⁺ + ν

This process is called beta plus decay.

(ii) The nucleus so formed is an isobar of  because the mass number is same, whereas the atomic numbers are different.