Quantum

What is a photon?

A quantum of electromagnetic energy

Work function

The minimum energy needed to remove a single electron from the surface of a particular metal

Threshold frequency (f₀)

The minimum frequency of the electromagnetic radiation that will cause the emission of an electron from the surface of a particular metal

Planck’s constant

6.63 × 10^-34 Js (in formula book)

Electron volt

• Energy transferred to or from an electron when it passes through a p.d. of 1 volt

• 1 eV = 1.60×10^-19J

Photoelectric effect

The emission of photoelectrons from a metal surface when electromagnetic radiation above a threshold frequency is incident on the metal

Photoelectron

Electrons emitted from the surface of a metal by the photoelectric effect

Evidence to suggest electromagnetic radiation is a wave

Evidence:

• It can difract, refract, and interfere with other EM radiation

Evidence to suggest light is a particle

Evidence:

• The photoelectric effect

Evidence to suggest electrons are waves

Evidence:

• They can be diffracted

Evidence to suggest electrons are particles

Evidence:

• They can be accelerated and deflected by magnetic and electric fields

Equation for photon energy in terms of frequency

E = hf

Equation for photon energy in terms of wavelength

E = hc/λ

Effect of increasing intensity of the light source while keeping the frequency constant on the photoelectric effect

If the frequency is greater than or equal to the threshold frequency:

• Increases the rate of emission of photoelectrons.

• Has no affect on their maximum KE

Otherwise, when less than the threshold frequency:

• No change; still no electrons emmitted

Eintstein’s photoelectric effect equation

hf = ϕ + KE_max

What must be true for the photoelctric effect to happen

Energy of photon > work function / frequency of EM radiation > threshold frequency

The behaviour of electrons which demonstrates that they have wave properties.

• When electrons are passed through a thin slice of graphite they produce circular interference fringes on a flourescent screen. This demontstrates they are diffracted.

• Diffraction of electrons occurs when the wavelength is similar to the gap size

• Changes in the electron's speed change the size and spacing of the rings

• Electrons have a (de Broglie) wavelength given by λ=h/p

How does increasing the electron’s speed/energy affect the circular interference pattern produced

• Higher speed/energy means the electrons hava a smaller de Broglie wavelength

• A smaller wavelength gives shorter path difference between areas of constructive and destructive interference

• As such the rings become closer together (not just ‘smaller’)

• They also become brighter because the electrons have more energy to transfer to the flourescent screen

How does decreasing the electron’s speed/energy affect the circular interference pattern produced

• Lower speed/energy means larger de Broglie wavelength

• Larger wavelength gives longer path difference between areas of constructive and destructive interference

• As such the rings become further apart

• They also become dimmer because the electrons have less energy to transfer to the flourescent screen

How is the work function related to the threshold frequency?

• A photon with less than the threshold frequency f₀ cannot cause electron emission

• As such work function = h (threshold frequency)

Explain how Einstein's theory explains the observations of the photoelectric effect and how they demonstrate the particle-like behaviour of electromagnetic waves.

• Individual photons are absorbed by individual electrons in the metal surface in a one to one interaction.

• Only photons with energies above the work function energy will cause photoelectron emission

• Photon energy is proportional to frequency

• Hence UV photons or blue photons with higher frequency have higher energy so will cause photoemission but red photons will not.

• A wave model does not explain a threshold frequency for emission to occur

• A wave model does not explain instantaneous emission of electrons.

• Number of electrons emitted depends on light intensity

• hf - ϕ = KE_max is the equation resulting from conservation of energy. This can be rearranged to get Einstein’s photoecetric effect equation.