QUANTUM WAVES

Evidence for the wave nature of electrons.

Diffraction is a wave property which occurs when waves pass through small gaps and spread out. Electrons passing through a crystal produce a diffraction pattern of rings, not a single spot, so must behave as waves.

de Broglie hypothesis

All particles have a wave-like nature and a particle-like nature

de Broglie equation

λ = h / p

Wavelength (m) = Planck constant / momentum (kgms^-1)

If you increase the pd, electrons travel...

Faster, so have a larger momentum (p = mv), smaller wavelength (λ = h / p) and smaller diffraction angles (nλ = dsinθ), resulting in a smaller ring radius. Voltage is inversely proportional to ring radius

Photon

A discrete packet of electromagnetic energy

E =

hf

Energy of a photon (J) = The Planck constant x Frequency (Hz)

Power of a beam =

nhf

Power (W) = No. of photons in a second x The Planck constant x Frequency (Hz)

The particle model of light

Light behaves like a stream of particles called photons, which each carry a discrete amount of energy, which is proportional to frequency. Higher intensity = more photons per second

Photoelectric effect

The emission of electrons from a metal when light above a certain frequency is shone on it due to them gaining energy

Photoelectron

An electron released through the photoelectric effect

Photoelectric effect gold leaf experiment

Charge builds up on the metal plate and spreads to the gold leaf. They will have the same charge, so will repel each other and the leaf will rise. If light is shone onto the metal, it will transfer energy to the electrons. If an electron gains enough energy, it will leave the surface, so charge is lost and the leaf will fall

How photoemission should occur according to the wave model

Delayed emission

Still emits eventually at a low emission

Energy of electrons build up over time

Electron KE increases with intensity

How photoemission actually occurs

Instantaneous emission

No emission below threshold frequency. If below this, the energy is re-emitted

One electron absorbs one photon

Electron KE increases with frequency

This is evidence for the particle model

Threshold frequency

The minimum frequency of light needed to liberate an electron via photoemission

Work function

Minimum energy required for photoelectric emission from the surface of a metal

ϕ =

hf₀

The photoelectric equation

hf = φ + KE(max)

The Planck constant x Frequency (Hz) = Work function (J) + Maximum kinetic energy (J)

On a graph of maximum KE against frequency, the y-intercept is...

- the work function

On a graph on KE against frequency, the gradient is...

The Planck constant

On a graph of maximum KE against frequency, the x-intercept is...

The threshold frequency

Not all electrons will have the maximum kinetic energy as...

Some will come from deeper in the metal and will lose energy via collisions

To convert from eV to J...

Multiply by 1.6x10^-19

To convert from J to eV...

Divide by 1.6x10^-19

Ground state

Lowest energy state of an atom

Excitation

When electrons absorb a photon and move to a higher energy level. Photon energy must be exactly equal to the difference between energy levels

De-excitation

The atom will now be unstable, so the electron emits a photon and moves to a lower energy level

For ionisation to occur, energy must be...

Greater than or equal to the work function

Absorption spectrum

Dark lines on a coloured background. Electrons are in discrete energy levels. A single photon interacts with a single electron, which will become excited. The photon energy = hf, so energy absorbed must be equal to an energy level difference. Frequency is inversely proportional to wavelength. Only certain transitions are possible, so only certain wavelengths are possible. There are specific wavelengths missing, so dark lines are formed

Emission spectrum

Coloured lines on a dark background. Electrons are in discrete energy levels. A single photon interacts with a single electron, which will become excited. It will then become de-excited, and emit a single photon. The photon energy = hf, so energy absorbed must be equal to an energy level difference. Frequency is inversely proportional to wavelength. Only certain transitions are possible, so only certain wavelengths are possible. Specific wavelengths are produced, so bright lines are formed