Lesson summary
12.1 Quantum Physics — AS PHYSICS 9702 notes: Describe photons, the photoelectric effect, wave–particle duality and atomic line spectra.Photon — a quantum (packet) of electromagnetic energy, with E = hf = hc/λ and h = 6.63 × 10⁻³⁴ J sQuantisation — energy is transferred in discre…
- Particle nature
- Electronvolt
- Photon momentum
- Definition
- Photoelectrons
- One photon, one electron
Section 1 of 10Photons
Photons
Photon
- Photon a quantum (packet) of electromagnetic energy, with E = hf = hc/λ and h = 6.63 × 10⁻³⁴ J s
Quantisation
- Quantisation energy is transferred in discrete packets, not continuously
Particle nature
- Particle nature the photoelectric effect and atomic line spectra can only be explained if radiation behaves as particles
Electronvolt
- Electronvolt the energy gained by an electron accelerated through a p.d. of 1 V, 1 eV = 1.60 × 10⁻¹⁹ J
Photon momentum
- Photon momentum p = E/c = h/λ, so radiation exerts pressure on a surface
Section 2 of 10The photoelectric effect
The photoelectric effect
Definition
- Definition the emission of electrons from the surface of a metal when electromagnetic radiation of high enough frequency is absorbed
Photoelectrons
- Photoelectrons the electrons emitted, which were already in the metal
One photon, one electron
- One photon, one electron each electron absorbs only one photon, and emission is instantaneous
Threshold
- Threshold only frequencies above the threshold frequency release electrons
Work function Φ
- Work function Φ the minimum energy needed to release an electron from the surface
Section 3 of 10Einstein's equation
Photoelectric equation
- Photoelectric equation hf = Φ + ½mv²_max
Threshold frequency
- Threshold frequency f₀ = Φ/h, and the threshold wavelength is λ₀ = hc/Φ
Below threshold
- Below threshold if hf is less than Φ, no electrons are emitted
Range of energies
- Range of energies electrons deeper in the metal lose energy on the way out, so most have kinetic energy below the maximum
Graph
- Ek(max) against f is a straight line with gradient h, x-intercept f₀ and y-intercept −Φ
Section 4 of 10Intensity and frequency
1Frequency sets the energy
- Frequency sets the energy the maximum kinetic energy depends only on frequency and work function
2Intensity sets the rate
- Intensity sets the rate at constant frequency, greater intensity means more photons per second,
- so a larger photoelectric current, with the same maximum kinetic energy
3Photoelectric current
- Photoelectric current proportional to the intensity at constant frequency
4Stopping potential
- Ek(max) = eV_s, and it is independent of intensity
Section 5 of 10Wave–particle duality
Wave–particle duality
Particle nature of light
- Particle nature of light shown by the photoelectric effect
Wave nature of light
- Wave nature of light shown by interference and diffraction
Failure of the wave theory
- Failure of the wave theory it predicts any frequency could eject electrons if exposure is long enough, a gradual energy build-up and kinetic energy rising with intensity, none of which is observed
Electron diffraction
- Electron diffraction electrons passed through a thin graphite film produce rings, showing matter has wave properties
Accelerating p.d.
- Accelerating p.d. a higher p.d. gives greater momentum, shorter wavelength and smaller rings
de Broglie wavelength
- λ = h/pWhat the symbols mean: λ = de Broglie wavelength (m) · h = 6.63 × 10−34 J s · p = momentum (kg m s−1) · m = mass (kg) · v = speed (m s−1)
Section 6 of 10Energy levels and line spectra
Discrete levels
- Discrete levels electrons in isolated atoms have only certain energies
Emission
- Emission a transition from E₁ to a lower level E₂ emits a photon with hf = E₁ − E₂, giving an emission line
Absorption
- Absorption white light through a cool gas has photons of matching energies absorbed, giving dark absorption lines
Unique spectra
- Unique spectra each element has its own set of lines
Larger energy gap
- Larger energy gap gives a shorter wavelength
Section 7 of 10Photoelectric sequence
1
A photon arrives with energy hf
2
One electron absorbs all of it
3
Energy Φ is used to escape the surface
4
The remainder is the electron's kinetic energy, at most hf − Φ
5
If hf is less than Φ, no emission occurs
Section 8 of 10More from the specification
- E = hf = Φ + EkmaxWhat the symbols mean: E = energy of one photon (J) · h = Planck constant (6.63 × 10−34 J s) · f = frequency (Hz)
Section 9 of 10Key terms
| Term | Meaning |
|---|---|
| Photon | a quantum of electromagnetic energy, E = hf |
| Work function | the minimum energy to release a photoelectron from a surface |
| Threshold frequency | the minimum frequency that causes photoelectric emission |
| Stopping potential | the p.d. that stops the most energetic photoelectrons |
| de Broglie wavelength | the wavelength of a particle, λ = h/p |
| Energy level | a discrete energy an electron in an atom can have |
Section 10 of 10Exam technique
1
Saying brighter light gives faster electrons — intensity changes the number of electrons, not their maximum energy.
2
Saying any frequency works if the light is intense enough — below the threshold frequency no electrons are emitted.
3
Forgetting that electrons absorb one photon each.
4
Mixing eV and J — convert with 1 eV = 1.60 × 10⁻¹⁹ J.