1202

Question 1

What experimental evidence is there that de Broglie’s postulate is correct? Why would this not be available for everyday objects?

Answer 1

electron diffraction

because de Broglie’s wavelength for everyday objects is really small and slit separation needs to be ≈ λ for diffraction => hard to achieve

Question 2

Which experiment implies that light is a wave? Why?

Answer 2

• Young’s double slit => interference is a wave nature of light, cannot be explained by classical particles since they can only go through one slit

Question 3

Which experiment implies that light is a particle? Why?

Answer 3

• Photoelectric effect
• below threshold frequency => not current flow but above current flow is proportionaly to threshold frequency
• this is because e- has min. binding energy (work function) => needed to liberate it from surface of material so it can travel around the circuit
• current proportional to intensity since e- absorb energy from 1 photon at a time => light is delivered in specific discrete amounts (like a particle)

Question 4

What is meant by photo excitation?

Answer 4

• Electrons excite by absorbing a photon, energy of photon must correspond to change in energy between 2 energy levels

Question 5

What is meant by recombination?

Answer 5

When free e- recombines with an ion so it is in an excited state => e- cascade down to ground level producing emission

Question 6

List three examples of astrophysical sources of absorption lines.

Answer 6

• Stellar atmospheres => outer layers (photosphere) absorb blackbody radiation from star
• Interstellar dust => emission from stars passes through gas cloud
• Intergalatic Lyα systems of clouds at different redshifts

Question 7

State Hubble’s law. Explain how Hubble’s constant can be used to roughly estimate age of universe? Why is the estimate only rough?

Answer 7

• The further away a galaxy is, the greater the redshift
• v=H₀d (recession velocity) [d = distance to galaxy]
• v=d/T => T=1/H₀
• Because the expansion of the universe is accelerating so the recession velocity is not actually constant hence Hubble’s constant is not actually constant => rough estimate

Question 8

Describe ways in which Bohr’s model improved from previous atomic models.

Answer 8

• atoms are stable
• Rydberg formula for spectral lines can be fully derived
• Rydberg constant expressed in terms of fundamental constants
• Bohr radius give “size scale” to atoms (useful order of magnitude estimation)
• “intuition” to quantum atomic models

Question 9

What is binding energy? And what is mass deficit?

Answer 9

• binding energy = energy released per fusion/fission event
• mass deficit = nuclear binding energy that holds nucleus together => mass deficit converted into energy by E=mc^2

Question 10

What is a galaxy? How are they classified?

Answer 10

• cosmic engines that turn gas → stars & stars → gas
• no significant stars formation occurs in intergalactic spce (outer space - void that exists between celestial bodies)
• classified by shapes and sizes

Question 11

How are spiral galaxies classified?

Answer 11

• Sa → Sc => large nucleus → small nucleus & tightly wounded spiral arms → loosely wounded spiral arms (more bulge → more disk)
• barred spirals are SBa, SBb, SBc
• spiral arms form at end of bars

Question 12

What are the non-classical assumptions made by Bohr in his model of the hydrogen atom?

Answer 12

• e- orbits are quantised & only orbits of specific radius are allowed by angular momentum quantisation rule

Question 13

How was de Broglie’s wavelength used to motivate Bohr’s assumption?

Answer 13

• λ=h/mv
• standing wave condition: circumference = whole number of wavelengths
• for H: 2πr=nλ_n
• n = principal quantum number
• angular momentum of e- in orbit: L=mvr =hr/λ = hr/[2πr/n] = (h/2π)n
• (h/2π)n is angular momentum quantisation rule

Question 14

How does the quantum model differ from Bohr model?

Answer 14

• e- is treated as a quantum particle
• calculate allowed energies & associated wavefunctions from TISE (need to solve 3D TISE to calculate allowed wavefunctions of e-s since H atom is 3D)

Question 15

What is the significance of quantum numbers n, l and m that arise in this solution? And what are the certain values that n, l and m can take? Which quantum number determines the energy of the electron?

Answer 15

• n, l and m are integers which index the wavefunctions
• n (principal quantum number - describe energy level): any non-zero non-negative integer
• l (orbital quantum number - describes subshell & gives orbital angular momentum): any non-negative integer ≦ n-1
• m (magnetic quantum number - describes specific orbital or “cloud” within that subshell): any integer where |m| ≦ l (L)
• n determines E of e-

Question 16

What additional quantum number needs to be introduced to fully describe properities of hydrogen atom?And what physical quantity does this extra quantum number correspond to?

Answer 16

• spin
• corresponds to angular momentum
• e- have intrinsic angular momentum (spin is internal property particles) => combined gives total spin angular momentum from all e-s
• Bosons have full integer spin whereas Fermions have half integer spin

Question 17

How would the world change if electrons were Bosons not Fermions?

Answer 17

• e-s can occupy same quantum states (since Pauli’s exclusion principle only applies to Fermions)
• since the most stable state is one with lowest energy level => all electrons would occupy ground state
• possibly collapse into the nucleus
• would not get absorption or emission lines

Question 18

What is the Doppler’s shift and how does it relate to redshift?

Answer 18

• redshift: z=v/c
• v = +ve => redshift = towards
• v = -ve => blueshift = away

Question 19

What is a Cepheid variable? Why do they make useful ‘standard candles’?

Answer 19

• a star that oscillates regularly between a larger, brighter state and a smaller, denser one = > luminosity varies regularly = periods of luminosity related to their absolute luminosity
• ‘standard candles’ are sources with known luminosity (=total power output)
• can time variability then predict its luminosity (absolute brightness) and use how bright it appears from Eartch to calcualte distance
• high luminosity so seen to large distances
• luminosity = constant * period of variability
• distance using luminosity and inverse square law of light (light sources further away => fainter so light spread over greater area so smaller power measured)

Question 20

What are the sequence of events believed to give rise to type Ia supernova? Why are type Ia supernovae useful ‘standard candles’?

Question 21

Describe observational properties that characterise AGN (active galactic nucleus) and give examples of an object containing an AGN.

Question 22

Summarise the processes powering an AGN.

Question 23

Give ways in which the Bohr model was inferior to QM models.

Answer 23

• only works for H
• not based on any underlying theory - no justifications for axioms
• is not QM
• e- is not a classical particle
• some features disproved by experiments e.g. finer features of atomic spectra (line spacing)
• angular momentum of ground state is zero not hbar

Question 24

What are the postulates of Bohr’s H atom?

Answer 24

1. e- travels in circular orbit around nucleus
2. e- orbit is stable and does not decay (as classical EM would predict)
3. only orbits where angular momentum l=nhbar are allowed (n = integer and hbar is reduced Planck’s constant)
4. e- can move to higher/lower E orbit by absorbing/emitting a photon of E=energy difference of the orbits

Question 25

What is de Broglie’s hypothesis? Describe one experiment that confirms the hypothesis? How can the results be used to determine the wavelength of matter waves?

Answer 25

• Matter should exhibit “wave-particle duality” just like photons
• λ = h/p (same relationship as photon momentum)
• electron diffraction - scattered electrons using two slits with slit separation about same size as wavelength => show that the intensity pattern had same structure as diffraction pattern from a grating
• and distance between peaks was consistent with de Broglie

Question 26

Describe process of quantum tunneling. How does quantum predictions differ from those of classical physics? Give physical processes in which this plays a role and its uses.

Answer 26

• wavefunction of particle is non-zero in finite barrier so possible for particle to “tunnel” through barrier
• even though its energy is such that it would not be able to overcome barrier classically
• radioactive decay - alpha particles tunnel through potential barrier hence probabilistic nature of radioactive decay
• uses: scanning tunnelling microscope (precise tool for measuring surfaces) - rate of current is proportional to tunnelling probability

Question 27

How to find solutions for infinite square well?

Answer 27

• The potential is infinite anywhere but within the well where the potential is 0
• Since no particle has infinite energy => ψ = 0 anywhere but within the well
• For wavefunction to be physical => needs to be continuous and normalised
• For wavefunction to be continuous => boundary conditions must match so ψ(0) = 0 & ψ(L) = 0
• sub in values for eqn for ψ to find constants
• n is not zero