Question $1(20$ marks$)$

$($a$)$ Sketch the crystal structure for simple cubic structure and body$-$centered cubic structure. $[5$ marks$]$

$($b$)$ The diamond lattice structure is the basic building block in silicon.

$($i$)$ Calculate the number of atoms in one cell of a diamond structure. $[5$ marks$]$

$($ii$)$ Calculate the density of atoms in silicon in terms of atoms $//$m$^(3).[5$ marks$]$

$($c$)$ The energy levels in the hydrogen atom as proposed by Bohr have discrete energy levels with principal quantum number n as shown in the figure below.

Given that the electron energy in the hydrogen atom, E$\_($n$)=-13\mathrm{.}6//$n$^(2)$eV$,$

Determine the energy released when an electron moves from energy levels E$\_(3)$ to E$\_(1).$