Quantum and nuclear physics

Question 1

Observations of the photoelectric effect showed that:

Answer 1

• below a certain threshold frequency (fo) of incident light no electrons were emitted, no matter how bright the light is (each metal has own fo)
• above fo the maximum Ek of the e is dependent on the frequency of the incident light
• if the intensity of the incident light is increased the freq. = same, more e were emitted but the energy of the e did not change
• there was no delay between the incident light arriving ad the e being emitted

Question 2

Why could these observations of photoelectric effect not be explained by light being a wave

Answer 2

• the energy of a wave is prop. to square of amplitude so a brighter more intense light should emit e with more energy
• the fo cannot be explained as by increasing intensity eventually enough energy should arrive so that e could be emitted no matter the freq.
• there should be a time delay between light arriving and e being emitted

Question 3

How were the observations from the photoelectric effect explained by Einstein

Answer 3

• e at the surface of the metal need a min amount of energy to escape (work function ø)
• incident light arrives in photons
• the energy of the photon depends on the frequency of the light
• the higher the intensity the more photons arrive per second but the energy level does NOT change
• e in the metal will absorb the photons but only ONE photon can be absorbed per e

Question 4

Stopping voltage

Answer 4

the value of voltage where the current is just zero as the electrical energy matches the Ek of the e
used to calc. Ek of e

Question 5

De Broglie Wavelength

Answer 5

proposed that particles should also have a wave nature as light could behave as a particle
it is dependent upon momentum
p = h/wavelength

Question 6

How did Davisson and Germer show that e could act as waves

Answer 6

they accelerated e at Ni and observed

expected:
- the Ni is rough on the microscopic level
- therefore the e were expected to be reflected diffusely (across a range of angles)

actual:
- the reflected e produced intensity peaks at specific angles depending on the potential difference used to accelerate the electrons

explained:
- the crystal surface acted as a diffraction grating causing the e to diffract and produce an interference pattern
- the angle of maximum e intensity was found to match that of the e’s calculated wavelength
wavelength = h/√(2meV)

Question 7

Bohr model of the atom

Answer 7

• e can exist in stationary states (i.e. remain in an orbit without emitting EM rad.)
• e can move between these states by absorbing or emitting a photon
  dif. in energy state is given by E = hf
• the angular momentum of an e in a stationary state is quantised in integral values of h/2pi

Question 8

Angular momentum

Answer 8

is the product of linear momentum and the radius of an orbit (mvr)

Question 9

Wavefunction

Answer 9

is the amplitude of the de Broglie wavelength
the wavefunction squared gives the probability per unit volume of finding the electron at that position (also called probability density)

Question 10

Similarities and differences in Bohr and Schrodinger’s models

Answer 10

similarity:
both have the same energy levels for e

differences:
- e location: Bohr has e in orbits of specific radii and Schrodinger has the wavefunction of the e determining the probability of finding it at any position
- nature of the e: Bohr has it as a particle and Schrodinger has it as a wave

Question 11

Heisenberg’s Uncertainty Principle

Answer 11

the simultaneous measurements of the position and momentum of a particle will always have some uncertainty

Question 12

What is quantum tunneling?

Answer 12

a process whereby quantum particles can overcome potential barriers deemed impossible according to classical physics
possible due to the wavefunction

Question 13

Factors that affect quantum tunneling

Answer 13

• the greater the mass of the particle the lower the prob.
• the greater the width of the barrier the lower the prob.
• the greater the energy dif. between the energy of the particle and the energy required to climb the barrier the lower the prob.

Question 14

Examples of quantum tunneling

Answer 14

Relatively low fusion that occurs in main sequence stars like the sun

alpha particle decay:
the strong nuclear force provides a potential barrier, the wavefunction of the alpha particle extends beyond the potential barrier allowing it to happen
radioactive substances with a long half-life have a higher and wider potential barrier than those with a short half-life

Question 15

Nuclear density

Answer 15

• assume nucleus is spherical,
  V = 4/3 pi R^3 = 4/3 pi Ro^3 A
• density = mass/volume = (A u)/(4/3 pi Ro^3 A)
  = (3 u)/(4 pi Ro^3)

therefore as all values in this formula are constant all nuclei have the same density

Question 16

Rutherford scattering and size of nucleus

Answer 16

as the alpha particle approaches it loses Ek and gaines Ep
at its closest approach all Ek has been converted to Ep
Ek = (kqQ)/r
r = (kQq)/Ek
this method not valid for smaller nuclei as the strong nuclear force becomes sig. and scattering deviates from expected pattern

Question 17

Electron diffraction and size of nucleus

Answer 17

gives more reliable values for size of atomic nuclei as e are leptons and hence not affected by the strong nuclear force but are still affected by positive charge of nucleus
if very high energy electrons are used they penetrate deep into the nucleus and scatter off quarks (deep inelastic scattering) and provides evidence for the quark model

Question 18

Evidence for nuclear energy levels

Answer 18

both alpha particles and gamma photons emitted during radioactive decay have been shown to possess discrete energy levels
however beta particles have a continuous spectrum (E total is discrete but is divided in varying proportions between the two particles)

Question 19

Decay constant def.

Answer 19

probability of a nucleus decaying per unit time