Each question is worth $20$ marks. $100$ marks total

The Bohr radius of an exciton in CdSe is $5\mathrm{.}4nm,$ whereas in CdTe the Bohr radius of an exciton is

$7\mathrm{.}3nm.$ If you have quantum dots of each material that are $3nm$ in diameter, how do you predict

the colour of light emission to compare between the two materials. Answer using no more than $4$

sentences. Pictures can be used to support your answer.

You are given a piece of silicon that has been doped to a level of $1{10}^{16}c{m}^{-3}$ with indium. $3$

a$.$ Calculate the number of majority carriers in the silicon. P type $1{10}^{{16}^{16}}$

b$.$ Are these carriers electrons or holes? holes

c$.$ If the silicon is doped with arsenic instead of indium, will the silicon be $n-$type, intrinsic, or

p$-$type?

$n$ type

d$.$ Let's now take the silicon from $($c$)$ that is doped with $($x$)1{10}^{16}c{m}^{-3}$ arsenic and further

dope it with $($y$)1{10}^{17}c{m}^{-3}$ more arsenic. Sketch graphs of the Fermi function, $f(E),$ for

each case, indicating the location of the Fermi level and the location of the edge of the

conduction and valence bands. Ensure that it is clear what the differences between the two

graphs are.

Below is a picture of a binary phase diagram that isn't possible. Using what you know about

solution thermodynamics, Gibbs free energy versus composition curves, and no more than $4$

sentences, explain why this phase diagram is not possible.Below is a picture of a binary phase diagram, which undergoes a process called a monotectic reaction upon cooling. Here, the monotectic reaction is:

$L_1+L_2$

a$.$ Label each region of the phase diagram with the phases that are stable at equilibrium.

b$.$ Sketch the Gibbs free energy curves of mixing just below, at$,$ and just above the temperature of the invariant phase transformation. Indicate on the $x-$axis of the free energy curves the locations of the phase boundaries and the phases present in each of the denoted regions.