(1) Let y(x, t) = Acos(kx −ωt). Show that
∂2y
∂x2=−k2y, ∂2y
∂t2=−ω2y(1)
(2) When a clean surface of silver is irradiated with light of wavelength 230nm,
the kinetic energy of the ejected electron is found to be 0.805eV. Calculate the work
function and the threshold frequency of silver.
(3) Express the Planck distribution law
ρν(T)dν=8πh
c3
ν3dν
ehν/kBT−1(2)
in terms of λand dλby using the relationship λν =c
(4) (Advanced Problem)
In this question you will calculate the theoretical and “experimental” de Broglie
wavelengths using a phenomenon known as the “Bragg reflection”
The de Broglie relationship is as follows:
λ=h
p(3)
where λis the wavelength, his Plank’s constant and pis momentum. In an electron
diffraction tube (Figure (1)), the electron are accelerated by applying a voltage (V)
(also referred to as a potential difference), which increases their kinetic energy (K).
When Vis small,
K=eV =p2
2m(4)
where eis the elementary electric charge and mis mass of an electron. The λmay
then be solved for to give,
λ=h
√2meV (5)
(i) Using the above equations, calculate the theoretical wavelength λof an elec-
tron which is accelerated through an electron diffraction tube of the 2500V voltage.
(ii) You will now use mock data to determine the experimental wavelength of an
electron based upon the diffraction pattern seen in the diffraction tube. In Figure
(2), you will notice how a beam of electrons is focused on graphite (indicated in
Figure (2) with a yellow square). Graphite is a crystal which contains two lattice
planes. The atoms in each plane reflect incoming radiation and have a distance d
between them, as shown in Figure () (d1=123pm and d2=213pm). These lattice
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