Quantum Phenomena

Electron-volt Photons

Energy levels

Wednesday 12 April 2023

The electronThompson was studying the conductivity of gases in fluorescent tubes

(neon) when he discovered the electron.

1) An electric current flows through a low pressure gas when a high potential difference is applied between two electrodes

2) The Cathode (negative electrode) gave off some invisible rays (Cathode rays)

3) These rays could be deflected by electric fields they were negatively charged particles called ELECTRONS.

AnodeCathode

Low pressure gas

Thermionic emissionIt is possible to produce electron emission from metals using low

voltage between the anode and the cathode.

1) The cathode has to be heated up to high temperatures (by a current flowing through a filament)

2) Electrons will escape from the filament (Cathode)

Cathode

Electrons

Thermionic emissionWhat would happen to the electrons if an anode (positive electrode) is

placed near the cathode?

1) The emitted electrons are attracted by the anode

2) The anode exerts a force on each electron the electrons gain K.E.

Cathode Anode

Vacuum

Electron deflectionSo, how did Thompson realised that the “cathode rays” are streams of

negative particles?The cathode rays could be deflected by electric, or magnetic fields.

Cathode Anode

Electrodes

Draw the path of the electrons that go through the hole in the anode and between the positive and negative electrodes.

Electron-voltWe can measure the Ek (Kinetic Energy) of a charge which is accelerated

across a potential difference using this formula:

QVEk Kinetic Energy (J) = Charge (C) x Voltage (V)

Kinetic Energy (J) = Charge (C) x Voltage (V)

The charge of the electron (elementary charge) is e = 1.60 x 10-19 C

So, we can define a new unit of energy, the ELECTRONVOLT:

JeV 191060.11 One electronvolt is the Kinetic Energy gained by an electron

when it is accelerated through a potential difference of one volt.

Neon LampsBut, why do fluorescent tubes emit light of different…

The gas that fills the tubes is different, so it emits different colour light when an electric current flows through it.

COLOURSAnd why do different gases emit different colours?

To answer this question we must understand the nature of light and electromagnetic radiation, and the structure of the atom.

Neon LampsShine the light from a light bulb and different gas lamps through a

prism. Then look at the spectra. What do you notice? What is the difference between the spectrum from the light bulb and the gas lamps?

• The light bulb gives a Continuous Spectrum.

• The gas lamps give a Line Spectrum.

• Each gas lamp gives different lines in their spectrum.

Continuous Spectrum

Line Spectrum

The Hydrogen SpectrumAll elements have their own line spectrum emitted when an electric

charge is passed through their vapour. For an hydrogen discharge tube this is the line spectrum we would obtain:

The lines on the spectrum are the wavelengths of the light produced by the discharge through a hydrogen gas.

What is this light made of?

656 nm

400

nm

500

nm

600

nm

700

nm

486 nm434 nm410 nm

The Photon: a massless particleWe’ve always thought of light as a wave, because it behaves like a wave

in many cases (e.g. refraction, reflection, diffraction…). However, Einstein discovered that in some instances light behaves like a particle. He called these “particles” PHOTONS. His observations extend to all electromagnetic waves.

What are they made of?

What are they made of?

What do they carry?

What do they carry?

How is the energy carried affected?

On what does their energy depend?

Representing a photonSo, why does a photon behave like a particle?

1) It is a packet of electromagnetic energy gives the idea of an “item” occupying a certain space, and not a continuum like a wave propagating in space

2) It travels in one direction only. So, a light bulb emits photons in all possible directions, with each photon travelling in one direction only.

3) The energy of a single photon is “quantized” and measurable. So, if a single photon hits a surface, it is a bit like a ball hitting a wall.

Photons emitted by filament lamp

Energy of a photonWe can measure the energy of a photon using Einstein’s equation:

h = 6.63 x 10-34 Js Planck constant

f = frequency of photon/electromagnetic radiation

c = 3 x 108 m/s speed of light in a vacuum

= wavelength of photon/electromagnetic radiation

hc

hfE

Energy LevelsSo, what causes the hydrogen in the discharge tube to emit just four

wavelengths of light?• The electrons in the atom can only orbit at certain distances from

the nucleus, i.e. the radius of the orbit is “quantized”

• Each “orbit” represents the energy of the electrons. So, electrons on the lower level (orbit) is at Ground State and have the lowest potential energy, while the other states are called Excited States because the electrons are at a higher potential energy

• The electric discharge gives the electrons the energy to jump on to higher energy levels

• Eventually (pretty quickly), these electrons will jump down to a lower energy level, or even the ground level

• In jumping down the electrons emit a photon of energy equal to the difference in the energy between the two levels

Energy Levels and Photon Emission

Calculate the energy of all the photons that can be emitted by this atom. E is the energy gap between two energy levels. Which of them is not part of the visible spectrum?

E = 0.66 eV

E = 1.90 eV

Ground State

1st Exited State

2nd Exited State

1st to ground state 2nd to 1st state 2nd to ground state

Answer: 1st to ground level• The energy of a photon is E = hf

• The energy of the emitted photon equals the energy gap between the two energy levels.

• E = 1.90 eV, so:

)(1059.4

1063.6

1060.190.190.190.1

114

34

19

Hzsf

Js

J

h

eVfhfeVE

Answer: 2nd to 1st level• The energy of a photon is E = hf

• The energy of the emitted photon equals the energy gap between the two energy levels.

• E = 0.66 eV, so:

)(1059.1

1063.6

1060.166.066.066.0

114

34

19

Hzsf

Js

J

h

eVfhfeVE

Answer: 2nd to ground level• The energy of a photon is E = hf

• The energy of the emitted photon equals the energy gap between the 2nd and the ground energy level.

• E = 1.90 + 0.66 = 2.56 eV, so:

)(1018.6

1063.6

1060.156.256.256.2

114

34

19

Hzsf

Js

J

h

eVfhfeVE