Q $1($a$)[8$ Marks$]$

$($i$)$ Calculate the frequency and wavelength of a photon of energy $3\mathrm{.}2$ eV$.$ Give you

answer in SI units. $[4]$

$($ii$)$ Calculate the wavenumber and wavelength of an electron with speed $4\mathrm{.}5106$

m$/$s$.$

Give your answer in SI units. $[4]$

Q $1($b$)[8$ Marks$]$

$($i$)$ Write down the Schr$$dinger equation and define all the terms. $[6]$

$($ii$)$ State the direction of travel of the particle represented by the wavefunction

$($x$,$ t$)$ expi$($kx$$t$)$ and write down the wavefunction for the free particle

travelling in the opposite direction. $[2]$