b$.$ Define Direct and Indirect band gap semiconductor with the help of E$-$k diagram giving an example of each. Consider the material alloy $I{n}_{0\mathrm{.}74}G{a}_{0\mathrm{.}26}A{s}_{0\mathrm{.}57}{P}_{0\mathrm{.}43},$ that is $x=0\mathrm{.}26$ and $y=0\mathrm{.}57$ in the general formula $I{n}_{1-x}G{a}_{x}A{s}_y{P}_{1-y}.$ Find $($a$)$ the band gap of this material and $($b$)$ the peak emission wavelength.

$[2+2+1$ Marks$]$