The colour of the $X_{2}$ molecules of group 17 elements changes gradually from yellow to violet dow

Question

The colour of the $X_{2}$ molecules of group 17 elements changes gradually from yellow to violet down the group. This is due to\

Professor PC Thomas Classes · Answer

$(\mathrm{b}, \mathrm{c}):$ Energy, $E=\frac{h c}{\lambda}$ The colour of the $X_{2}$ molecule of group 17 elements changes gradually from yellow to violet down the group. This is because the amount of energy required for the excitation of the halogen atom decreases down the group from $F_{2}$ to $I_{2}$. $\operatorname{HOMO}\left(\pi^{*}ight)$-LUMO $\left(\sigma^{*}ight)$ gap decreases down the group that makes $\pi^{*}$ to $\sigma^{*}$ excitation easier. Lesser the energy gap, more is the wavelength of light absorbed and hence, lesser is the wavelength of light emitted.\