Quantum Mechanics (all topics) Flashcards
What is the equation for linear momentum?
p=mv
How is speed defined?
Magnitude of velocity
What is Newton’s second law of momentum?
rate of change of momentum is equal to force acting on the particle
What is acceleration?
Second derivative of r (position vector) with respect to time
What are equations for kinetic energy?
E=p^2/m=1/2mv^2
What are harmonic oscilator equations?
F=-kx
V=1/2kx^2
Etot=1/2mvmax^2
How is angular momentum J defined?
J=rxp (vector quantities)
For what type of radiation does classical mechanics fail?
Black body radiation
How is black body radiation defined?
An object capable of absorbing all frequencies of radiation uniformly
For what wavelengths does Raleigh-Jeans law fall short?
For short wavelengths
How can the experimental observation for black body radiation be rationalised?
By quantisation of energy
What evidence is there for the quantisation of energy apart from black body radiation?
Discrete absorption and emission spectra of atoms and molecules
What is the quantisation of energy equation?
E=nhv (permitted energies are integer values of hv)
How can light be described classically as a quantum description?
Classic: as a wave (EM)
Quantum: as particles called photons
What is the equation connecting the properties of waves?
lambda x v=c
Are EM waves transverse or longitudinal?
Transverse
What phenomena leads to diffraction?
wave interference
What experiment lead to the wave character of particles?
Davisson and Germer (1925)
What is the de Brogelie equation?
lambda = h/p
how is probability density related to the wave function?
absolute value squared
how are operator, eigenvalue and eigenfunction related?
operator x eigenfunction= eigenvalue x eigenfunction
what is the normalisation of the wave function?
probability density = 1
For a normalised wave function how do we obtain the expectation value?
w1 square modulus of c1 + w2 square modulus of c2 and so on…
What is Heisenberg uncertainty principle?
It is impossible to state simultaneously the momentum and position of a particle
What is the difference between fermions and bosons?
Bosons have symmetric wavefunctions
Fermions have anti-symmetric wavefunctions
Give an example of a fermion and a boson?
Fermion: electron, neutron
Boson: helium atom, alpha particle
What do l and m refer to?
l is orbital angular quantum number
m is magnetic quantum number
How is m related to l?
permitted values of m are 2l+1
What factors do radial wave functions depend on?
n and l but not (ml)
Where do the two terms in the Veff equation come from?
columbic and centrifugal force
What is a hydrogen atom?
a one electron atom or ion
Describe the Stern-Gerlach experiment?
A beam of Ag atoms through a magnetic field. Two bands of Ag atoms observed. The observation led to the phenomenon being defined as ‘spin’.
What are the spins of fermions and bosons?
fermions = 1/2 integral spins bosons= integral spins (including 0)
What is needed to fully specify the state of a hydrogen atom?
n, l, ml and ms
What are the selection rules for a photon?
delta l = +-1
deltaml = 0, +-1
Account for change in angular momentum occurring with emission of a photon
Why is the SE for many electron atoms complex?
Interactions between electrons
What is Pauli Exclusion Principle?
2 electrons per orbital and spins must be paired
What is the Pauli exclusion principle in terms of fermions and bosons?
Fermions wavefunction changes sign when 2 labels of identical fermions exchanged.
Wavefunction stays the same for identical bosons
What is Hund’s rule?
atom in its ground state maximises unpaired electrons
Why is 4s orbital occupied before 3d?
The total energy is lower when this configuration is adopted
How is shielding constant defined?
Z-Zeff
How does Zeff arise?
From columbic repulsion of electrons. Equivalent to a negative point charge located at nucleus.
How many triplet states are there?
3
Which is lower in energy: triplet or singlet state?
Triplet state
How does spin-orbit coupling arise?
From the interaction of the magnetic field created by orbital angular momentum and the magnetic moment created by orbital spin moment. Strength of coupling depends on orientation of momenta.
What do orthohelium and parahelium refer to?
Parahelium is singlet state. Orthohelium is triplet state
Is an antiparallel or parallel arrangement of ml and ms preferred?
Antiparallel maximises interaction
What does J refer to? What are the values of J with regards to l
Total angular momentum and is a sum of ms and ml (vector sum can be represented by diagrams)
J=l+1/2 or l-1/2
Does A (spin-orbit coupling constant) increase or decrease with atomic number, Z?
Increases, it increases with nuclear charge and hence atomic number Z. (Z^4 increase)
Why are fine spectral lines observed for atoms?
Spin-orbit coupling gives rise to fine spectral lines
Describe how term symbols are denoted for an atom?
multiplicity of term (2S+1), total orbital angular momentum (L) from Clebsch-Gordon series, total angular momentum (J) from Russell Saunders
What happens the Russell-Saunders series for heavy atoms?
It fails in heavy atoms, as spin-orbit coupling is large and j-j coupling occurs.
What S values give rise to a singlet, doublet and triplet?
S=0 is singlet S=1/2 is doublet S=1 is triplet
Where do selection rules arise for transitions?
Conservation of angular momentum and fact photon has spin 1 (boson)
What are the quantum selection rules?
delta S= 0
delta L=0, +-1
delta J= 0, +-1
Are selection rules for Russell-Saunders and what happens to heavier atoms?
Yes, for russell sanders. For heavier rules progressively fail, delta S= +-1 allowed therefore as j-j arises.
How are transitions written?
Lower term to upper term
