1

Energy Levels and Quanta

2

Energy LevelsPlank’s and Einstein’s quantum theory of light gives the key to understanding the regular patterns in line spectraPhotons in these line spectra have certain energy values, so electrons in those atoms can only certain energy values.The energy level diagram shows a very simple case – it is for an atom in which there are only two possible energy levels,

Excited state

Ground state

Photon emitted

Electron, shown by the blue dot has the most potential energy when it is on upper level, or excited state.On the lower level, or ground state, it has the least potential energy

3

Energy levels and quantaDiagram shows electron in excited atom dropping from excited state to ground state.

This energy jump (transition) has to be done as one jump and is the smallest amount of energy this atom can lose – called a quantum (plural = quanta)

Potential energy electron has lost is given out as a photon.From E = hf (or E = hc/λ) this energy jump corresponds to a specific frequency (or wavelength) corresponding a specific line in the line spectrum.

In an atom, ground state and each subsequent excited state correspond to a particular electron shell (or energy level).

4

Energy levels and quantaThe diagram shows an atom with 3 electron energy levels. What are the photon energies, in eV that this atom can emit?

10 eV

5 eV

n = 1

n = 2

n = 3

The potential wellIf you fell down a pit of depth 3m, you would lose about 2000 J of potential energy (always calculated from ground level = zero pe)

At the bottom of the pit, your Ep is 2000 J less than zero: it is – 2000 JYou could not jump out, as the maximum kinetic energy you could generate is 1300 JYour total energy would be 1300 J + (-2000 J) = -700 J

5

The potential wellIf the sum of Ek + Ep is negative, we say that the system is bound. You are stuck in the pit.This situation is described as the potential well

Similar situation occurs in an atom. To remove an electron completely from an atom, enough energy must be supplied for the electron to jump from ground state to the very top of the potential well.

It’s the energy needed to overcome the attraction of the nucleus and is called ionisation energy

6

Energy levels of hydrogenA Danish physicist called Neils Bohr found that hydrogen spectrum could be explained by a set of energy levelsLowest energy level is the ground state, all the others are excited states.

Ground state is a long way below the excited states.And excited states get closer together as you go upwards

n = ∞

n = 4n = 3

n = 2

n = 1

E = 0

E =-0.85eV

E =-1.51eV

E =-3.04eV

E =-13.61eV

7

Energy levels of hydrogenLooking at the energy values of each level: the electron is bound to the atom – does not have enough energy to get out.

It requires extra energy to leave the hydrogen atom.Zero potential energy occurs at the very top, electron escapes and leaves an ionised atom.

The potential energy of all the levels below E = 0 are negative

Use the diagram on slide 6 to find the ionisation of hydrogenIE = energy of highest level – energy of ground state= 0 eV – (-13.61 eV) = +13 61 eV

8

Hydrogen emission spectrum

The simple energy level diagram on slide 2 has only one possible energy jump – from excited to ground state.Diagram on slide 4 has 3 energy levels and 3 possible energy jumps In hydrogen with all those energy levels, there are many possible transitions

Look at the diagram below

9

Arrows all show downward energy transitions, so each would give out a photon – diagram called an emission line spectrumTransitions on the left – going down to ground state, are all large. Known as the Lyman series, giving out energetic photons in UV region of the spectrum.

Smaller transitions on the right to n=3 energy level, give out less energetic IR photons. Known as Paschen seriesBetween these two sets is the Balmer series of lines going to the n=2 energy level.This series includes the 4 visible lines in the hydrogen emission spectrum, coloured in the diagram.

Emission spectra result in electrons dropping down to lower energy levels – where did the electron get this energy from in the first place?One way is to absorb a photon.

10

Absorption spectraExcited state

Ground state

Photon absorbed

The diagram shows absorption in a simple two-energy level atomExact opposite of emission spectra, electron starts in a lower energy level, absorbs a photon, which raises it to the excited state.

Photon must exactly match the energy jump

A hydrogen atom has its electron in the energy level at -1.51 eV. It absorbs a photon, which promotes it to the -0.85 eV level. What is the wavelength of this photon.Answer is1.9 x 10-6 m (infra-red region)

11

Absorption and emission spectrum of hydrogen

12

The Sun’s spectrumThe first place an absorption spectrum was observed was in sunlight. Continuous spectrum from the Sun is covered with vertical dark lines.

These were measured and classified by Joseph Fraunhofer – Bavarian instrument maker.

Lines due to cooler gases in the outer layers of the Sun

13

Light from the hot photosphere passes out from the Sun, some light is absorbed by these cooler atoms.

Promotes their electrons to excited states. Absorbed photons must match energy jumps exactly – only certain wavelengths are absorbed.

These absorbed photons are re-emitted later in all possible directions – so fewer photons end up going directly outwards.

Spectrum of light becomes dimmer at these wavelengths, because fewer photons are reaching us – giving dark lines.Such spectra are extremely useful for astronomersAbsorption lines in the spectrum of a star or galaxy give us a ‘fingerprint’ of the elements present.

Stimulated emission• In his analysis of quantum theory, Einstein

realised that emission and absorption were not the only possible way to make energy jumps.

• An atom already in the excited state can be ‘persuaded’ to emit a photon.

• Done by a passing photon of exactly the same energy.

• Produces two identical photons – original one and the one created by downward transition of the electron.

• 1st photon stimulated the atom into emitting a second photon – called stimulated emission.

15

This photon stimulates the atom...

...to emit an identical photon

Such a beam of light containing identical photons is monochromatic

Light is also coherent – phase is constant across the beamThis way of producing extremely regular, uniform radiation was first done with microwaves.

A more interesting application uses photons in or near the optical range – called a laser

Light Amplification by Stimulated Emission of RadiationSince their invention in 1958, lasers have become very common – in every CD player and DVD player

16

Laser light is a narrow, parallel beam which is very intense – scientific usefulness is due to two facts.

1. Light is monochromatic – one wavelength only2. Light is coherent – all the waves are in step.

Laser action ‘lasing’ can take place in solids, liquids and gases.

Before stimulated emission can happen, there must be more atoms with electrons in the higher excited states than in ground state.

Under normal circumstances this is the other way round – electrons need to be ‘pumped’ up to the excited state.Often done using an electric field (helium-neon gas laser)See diagram on the board.

17

One of the excited atoms emits a photon, at random.

This photon stimulates another emission. These two photons then stimulate another two emissionsThis rapidly becomes an avalanche of identical photons

Mirrors at each end reflect the light, making photons pass to and from along the laser.

One mirror is partially silvered, so small % of photons can continually escape as a laser beam.