Show that for an isotropic radiator, the directive gain is equal to unity.

An isotropic radiator radiates efficiently in all possible directions. 

The directive gain of an isotropic radiator depends on the beam solid angle and it can be expressed as

$D=\frac{4\pi }{{\Omega }_A}--->\left(1\right)$ where ${\Omega }_A$ is the beam solid angle in steradians. 

Since an isotropic radiator radiates in all possible directions, the beam solid angle for an isotropic radiator will be

${\Omega }_A=4\pi \mathrm{steradian}$