1. Atoms can exist in discrete energy levels called quantum states. Electrons in atoms can only have certain energies corresponding to these levels. 2. When an electron in an excited state drops to a lower energy state, it emits a photon. The energy of the photon equals the energy difference between the states. 3. Absorption is the reverse process, where an electron absorbs a photon and jumps to a higher energy state. Emission and absorption spectra reveal the possible energy transitions in atoms.

1. Energy Levels and Quanta
1

2. Energy Levels
Plank’s and Einstein’s quantum theory of light gives the
key to understanding the regular patterns in line spectra
Photons 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
2

3. Energy levels and quanta
Diagram 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).
3

4. Energy levels and quanta
The 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 well
If 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 J
You could not jump out, as the maximum kinetic energy
you could generate is 1300 J
Your total energy would be 1300 J + (-2000 J) = -700 J
4

5. The potential well
If 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
5

6. Energy levels of hydrogen
A Danish physicist called Neils
Bohr found that hydrogen
spectrum could be explained
by a set of energy levels
Lowest 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 = 4
n = 3
n = 2
n = 1
E = 0
E =-0.85eV
E =-1.51eV
E =-3.04eV
E =-13.61eV
6

7. Energy levels of hydrogen
Looking 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
hydrogen
7
IE = energy of highest level – energy of ground state
= 0 eV – (-13.61 eV) = +13 61 eV

8. Hydrogen emission spectrum
8
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. 9
Arrows all show downward energy transitions, so each would
give out a photon – diagram called an emission line spectrum
Transitions 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 series
Between 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 spectra
10
Excited
state
Ground
state
Photon
absorbed
The diagram shows absorption in
a simple two-energy level atom
Exact 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. 11
Absorption and emission spectrum of hydrogen

12. The Sun’s spectrum
12
The 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. 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 astronomers
Absorption lines in the spectrum of a star or galaxy give
us a ‘fingerprint’ of the elements present.

14. 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. 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 beam
This 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 Radiation
Since their invention in 1958, lasers have become very
common – in every CD player and DVD player

16. 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 only
2. 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. 17
One of the excited atoms
emits a photon, at random.
This photon stimulates
another emission. These two
photons then stimulate
another two emissions
This 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.