Chemistry - GOC Question with Solution | TestHub

${\mu }_R=\sqrt{{\mu }_1^2+{\mu }_2^2+2{\mu }_1{\mu }_2\cos \theta }$

If ${\mu }_1={\mu }_2$, the formula simplifies to:

${\mu }_R=\sqrt{2{\mu }_1^2(1+\cos \theta )}$

This can be further simplified using the identity $1+\cos \theta =2{\cos }^2(\theta /2)$:

${\mu }_R=\sqrt{2{\mu }_1^2(2{\cos }^2(\theta /2))}=\sqrt{4{\mu }_1^2{\cos }^2(\theta /2)}=2{\mu }_1\cos (\theta /2)$

In the context of the given molecules, the $-C{H}_3$ group is an electron-releasing group.