Atomic Physics Flashcards
What is the Stark Effect?
is the shifting & splitting of spectral lines from atoms due to an external static electric field
What is the linear stark effect, what conditions must it satisfy? Discuss which conditions the energy correction varies linearly with electric field? Why can hydrogen atoms display a linear stark effect & under what conditions?
- Linear stark effect is the case where the shifting of the spectral lines is linear in the strength of the applied field.
- delta E is calculated in perturbation theory from matrix elements of r * E
- in the ground state (only 1 eigenstate, Y_0) <Y_0| r * E|Y_1> vanishes by spherical symmetry, no linear dependence seen
- If H atom is excited, there’s several degenerate eigenstates Y_1 with the same unperturbed energy, the linear stark effect is seen from diagonalising <Y_i|r * E|Y_1>
Explain why classically we might see a quadratic stark effect?
Classically applying an E field induces a dipole on the proton & electron. This acts with the field to lower the energy of the atom so the shift is of the form.
(delta)E = -d * E (alpha) -E^2
State all the selection rules for electric dipole optical transition
(delta) J = +/- 1,0 but not 0 –> 0
(delta) L = +/- 1,0 but not 0 –> 0
(delta) S = 0
(delta) l = +/- 1,0
(delta) m_j = +/- 1,0
only 1 electron may change its configuration
Explain the meaning of all the selection rules
J - total angular momentum
L - Total orbital angular momentum
S - total spin angular momentum
l - orbital angular momentum of e~
m_j - magnetic quantum number
Why is there no selection rule for n and why are (delta)n =0 allowed?
n (principle quantum number) doesn’t directly affect angular momentum or spin of the atom, so changes in n don’t violate any conservation laws. (delta)n=0 is allowed because changes in l or m_j can occur without necessarily changing n
What are the possible values of angular momentum quantum number, j, for l=1, s=1?
range of j = (|L-S|… L+S)
Why is (delta)l=0 allowed?
transition rules apply to transitions involving a change in electronic states, this doesn’t necessarily mean orbital angular momentum has to change
What mechanism gives rise to spin orbit correction?
In the rest frame of the nucleus, e~ produces a E field, and in the rest frame of e~ this E field is transformed into a B field. The magnitude of B is proportional to the rate of e~ orbit and hence orbital angular momentum l. The magnetic moment of e~ is proportional to S. and in the presence of a B field has energy -N*B and therefore e~ of H atom that proportional to l * s
What’s the effect of spin orbit correction on the quantum numbers used to label
states? What effect does the spin orbit correction have on choice of quantum
numbers?
m_l and m_S are no longer good quantum numbers and are replaced by j and m_j which are associated with total angular momentum and the z of total angular momentum
State the requirements for an emission line to be in the lyman, balmer and
paschen series and their approximate wavelengths.
Lyman - n_x –> n_1 IR wavelengths
Balmer - n_x –> n_2 Visible wavelengths
Paschen - n_x –> n_3 UV wavelengths
Talk about parahelium and orthohelium, in the context of electron-electron
interactions being considered as a perturbation
An effect of the exchange term is that the energy of the helium atom depends on its spin states. The S=0 state (parahelium) couples to the symetric eigenfunction
S-1 (Orthohelium) couples to antisymmetric spatial eigenfunction in the first order, (delta)E (1) = E_direct +/- E_exchange. + for s=0 and - for s=1
What physical quantities are described by einstein Aij and Bij coeeficients?
Aij —-> Probability of spontaneous emission of an atom is an excited state
Bij —-> Probability of a stimulated emission event
Bji —-> Probability of absorption
What is requires in QM for a quantity to be conserved?
For a conserved quantity, the operator associated with its observable must commute with the Hamiltonian of the system. P_x = ihd/dx must commute with H.
What is the expansion theorem in quantum mechanics and what properties of
the eigenstates of a Hermitian operator are usually used to calculate any
particular expansion?
The expansion theorem is that the general state of the system can be represented by a unique combination of the eigenstates of any Hermitian operator calculated with the same boundary conditions as the general state.
The properties used are orthonormality and orthogonality.
In the context of helium, explain what the exchange energy is and how to
calculate at first order
The exchange energy arises from the requirement that eigenfunctions must respect exchange symmetry. the total wavefunction for both e~ in helium must be antisymmetric. e~ e~ repulsion is treated as a perturbation
+ for S=0 (parahelium) (1s1s)
- for S=1 (orthohelium) (1s2s)
Why are the first ionisation energies of a Helium atom with one excited electron
very similar to the corresponding ionisation energies of a Hydrogen atom?
the excited electron spends all its time outside the unexcited wavefunction a spherical gaussian surface through the position if the excited electron has a charge of +1 so the e~ will see the nucleus and inner e~ as a hydrogen nucleus. So the field experienced by the excited e~ is almost identical to that of an e~ orbiting a hydrogen nucleus so that they have similar energy levels.
The energy levels for the outer electron in an alkali metal atom are well
approximated by
E, = (-Ry)/(n- 6),
Isis
where Ry is the Rydberg energy and 6j is the quantum defect. What is the
physical reason for the quantum defect? How does the quantum defect
vary with angular momentum and why?
The outer e~ alkali metals spends most their time outside the inner electrons therefore outer e~ experiences a potential close to that of a hydrogen nucleus. But for smaller angular momentum states it spends some of its time inside the screening electrons. The energy levels are lower than that of hydrogen nucleus. This is the reason for the defect.
Why does quantum defect vary with angular momentum?
The quantum defect decreases with increasing angular momentum.
High angular momentum states have a smaller probability of being found inside the shielding electrons due to centrifugal energy.
Explain why the quantum defect for l= 0 orbitals is larger than that for | > 0
orbitals.
Because the shielding of the nucleus from inner electrons is greater than 1, so there’s more of a deviation from hydrogen like energy levels
State Hund’s rules.
- within constraints of pauli exclusion, the level with more multiplicity (Max S) is the lowest energy. Ensures that as many electrons as possible have parallel spins, reducing e~ to e~ repulsion.
- within constraints of the first rule and pauli, the energy level with more orbital angular momentum (L) is lowest in energy. Rule minimises e~ repulsion by maximising spatial separation.
- For subshells less that half filled the term with smallest total angular momentum (J=|L+S|) is the lowest in energy. For subshells more that half full (J=L+S) is lowest in energy. For exactly half full J=S as L=0
