quantum physics

De Broglie hypothesis

All particles have wave-like nature and particle-like nature. The wavelength of a particle is inversely proportional to the particles momentum

Define de Broglie wavelength

Wavelength associated with a moving particle

Link between wavelength and increase in pd

• higher pd = higher momentum

• Higher p (h/wavelength), decrease wavelength

• Decrease wavelength decreases diffraction angle

• Or lower fringe spacing in diffraction pattern

Electron volt

Kinetic energy gained by one electron that is accelerated through a potential difference of 1 volt. = 1.6 ×10^-19 J

Intensity

Power transferred by a wave per unit area

Photoelectric effect

When light of a high enough energy shone on a metal surface causes electrons to be emitted. The electrons are given enough kinetic energy by the photons to overcome attractive force of ions in metal

1 incident photon emits 1 photo electron

• Photon of energy E = hf

• Absorbed by electron

• Some of energy used to escape (work function), rest is kinetic energy

• If photon absorbed by electron lower in energy well, escaping electron has lower ke than kemax

When f = threshold f,

E = work function

Photoelectric effect rules

• Electrons from surface of metal removed

• 1 photon to 1 electron

• Electron removed instantaneously on incidence of photon

• Energy must be conserved with interaction

• Increasing intensity of radiation does not release single electron if threshold frequency not met - intensity proportional to rate of emission of electrons/arrival of photons

Photon

Discrete packet (quantum) of electromagnetic energy/radiation

Planck’s constant

Constant that relates energy of photon to frequency (h = 6.63 ×10^-34)

Threshold frequency

Minimum frequency of incident EM radiation needed to cause electrons to be emitted from surface of metal in the photoelectric effect (regardless of intensity)

Threshold wavelength

c = f x wavelength

• longest wavelength possible for emission of electrons

Work function

Minimum energy required of EM radiation to remove an electron from a metals surface

Equation for accelerating charged particle through potential difference V

eV = ½ mv²

• Can rearrange for speed

Equation for energy of photon

E = hf

OR if at speed of light

E = (hc)/wavelength

Conversion to eV + definition

Kinetic energy of one electron after acceleration from rest in potential difference of 1v

eV = p.d. x 1.6 ×10^-19

eV = joules / 1.6 × 10^-19

Equation for De Broglie wavelength for diffraction

Wavelength = h/(mv) = h/p

Equation for photoelectric effect

E = work function + Ek(max)

Where Ek(max) = 1/2 mv²

Evidence for particulate and wave like nature of electromagnetic radiation

• Photoelectric effect for particulate nature

• Interference and diffraction for wave nature

Why are most electrons emitted at kinetic energies less than the maximum

Maximum kinetic energy only applies to electrons at the surface

• Electrons deeper inside lose energy due to collisions when escaping

Why does rate of emission of electrons change as frequency of incident light increases (constant intensity light)

• Increase frequency of incident light increases= increase energy (E = hf)

• Since intensity is constant (power /area), power = energy/time, increasing energy of photons means less photons per unit time hit metal surface to keep intensity constant

• 1 photon emits 1 electron, less emissions

Evidence provided by photoelectric effect for particulate nature of EM radiation

• No time delay between illumination and emission

• Max. Kinetic energy is dependent on frequency of incident EM radiation

• Maximum kinetic energy is independent of intensity

Why do dark lines occur on the spectrum of light emerging from photoelectric effect

• Electrons have discrete energy levels (1 electron to 1 photon)

• Electrons absorbs photons and become excited

• Energy absorbed must equal the difference in energy levels

• E = hf, meaning the photon needs to be a specific frequency to equal the exact energy to jump

• Electron de-excites and emits photons in any direction

Photon energy + energy level equation

hf = E1 - E2

Relationship between jump in energy level and frequency/wavelength

Larger E = smaller wavelength

Larger E = larger wavelength

Why there is a single frequency of EM radiation for a single transition

Transition emits photon when E = difference in energy levels

Frequency of radiation must correspond with the energy of the photon

Equation for momentum, energy and speed

p = e/c