The Zeeman Effect & Electron Spin Flashcards
What is the zeeman effect?
Where an external magnetic field “lifts the degeneracy” of the l-states in the H-like atom: single energy level splits to 2l+1 levels
What does a 1D graph of ω look like without and with an applied B-field and what are its characteristics?
Zero B-field, single spike in middle centred at ω0. With applied B-field, 3 spikes with middle one at ω0 and one either side at +/- ω(L), the Larmor frequency.
What is the equation for the Larmor frequency, ω(L)?
ω(L) = eV/2m(e)
What is the equation for ΔE, the energy change of the split energy levels?
ΔE = +/-ћω(L) = +/- μ(B)*B, where μ(B) = eћ/2m(e) = Bohr Magneton
What do the split spectra always comprise of? Why is this?
3 lines even if the state has l >= 2. Due to a second selection rule: Δm(l) = 0, +/- 1
What is the equation for the z-component of the magnetic moment of the electron?
μ(z) = -e/2m(e) Lz
What is the splitting of a spectral line into 3 frequencies (or wavelengths)?
The Normal Zeeman Effect
What is the anomalous zeeman effect?
Where spectra have more complicated patterns of splitting (not just simple +/- ω(L) rule)
What is spin?
Spin is another form on angular momentum intrinsic to particles.
What values can the spin quantum number take?
Half-integer values
What is the equation for the spin angular momentum component along the z-axis?
s(z) = +/- 1/2 *ћ
What is the equation for the magnitude of the spin angular momentum s?
s = ћ*sqrt(s(s+1)) = sqrt(3)/2 *ћ
What is the equation for the total angular moment J?
J = L + S, where L is the orbital angular momentum and S is the spin angular momentum.
How can we define a total angular momentum quantum number?
|J| = ћ*sqrt(j(j+1)), j = | l+/- 1.2 |
What is the equation for the z component of the total angular moment J(z)?
J(z) = ћ*m(j), where m(j) = 0, +/-1, ….. +/- j
What happens when j = l+1/2 and when j = l-1/2?
j=l+1/2: L and S have a parallel z-component, j=l-1/2: L and S have anti-parallel z-component.
What are the new selection rules for the total angular momentum quantum number j?
Δj = +/- 1, Δm(j) = 0, +/-1
In the Stern-Gerlach experiment, how were the Silver atoms given kinetic energy?
Provided by thermal energy from the furnace used to sublimate the material.
What was done with the silver after it was given KE in the Stern-Gerlach experiment/
Beam collimated and travels along flight tube, all in vacuum. Normally, beam would simply splat on to a detector in a single stripe due to the shape of the collimator.
What was used in the Stern-Gerlach experiment to creat an inhomogeneous magnetic field?
Pair of specifically shaped magnetic pole pieces inserted across flight tube to generate the B-field.
What was the surprising result of the Stern-Gerlach experiment? Why did this happen?
Beam split into two rather than an odd number 2l+1 stripes. This is explained by hypothesising intrinsic angular momentum of the atom with half-integer spin, so that 2s+1 = 2.
What is the equation for ΔLi, the change in angular momentum for a small element of mass and charge?
ΔLi = ri x Δpi, where ri is the radius of the circle around the axis
What does each element of mass and each element of charge contribute to for a classical charged entity?
Each element of mass contributes to the angular momentum. Each element of charge contributes to the magnetic moment.
What is the equation for L(total)?
L(total) = sum over i of ri x Δpi
What is the equation for μ(total)?
μ(total) = sum over i of Δqi/2mi *ri x Δpi
What is a simple way of writing the magnetic moment μ?
μ = -q/2m *gL, where q is the total charge and m is the total mass and g is a dimensionless quantity called Gyromagnetic ratio.
What is the equation for the total magnetic moment vector for an electron?
μ = -e/2m(e) *(L +gs), where s is the spin
What can we learn from looking at the electrons frame of reference in the nucleus? What is the phenomena called?
The electron ‘sees’ a current loop due to the nucleus. The B-field due to the ‘orbiting’ nucleus interacts with the electrons spin magnetic moment. Called spin-orbit coupling.
What is the equation for the spin-orbit interaction energy, V(mag)?
V(mag) = -μ(s).B, where B is the B-field
Since spin can have 2 possible orientations, what does this mean for the degeneracy?
The spin-orbit coupling can lift the degeneracy of spin states (can make an up magnetic moment or a down magnetic moment depending on the spin).
What is meant by fine structure?
Where external magnetic fields and SOC give rise to changes in optical spectra.
