1. Unit 2 Particles and Waves Spectra
CfE Higher Physics
Unit 2
Particles and Waves
Spectra

2. Learning Intentions
State that electrons in a free atom occupy discrete energy levels
Draw a diagram which represents qualitatively the energy levels of a hydrogen atom
Use the following terms correctly in context: ground state, excited state, ionisation level

3. Continuous and Line Spectra
A continuous spectrum contains all the possible frequencies of radiation:
In a line spectrum only certain frequencies are present:
emission spectrum
absorption spectrum
Line spectra can be explained by the organisation of electrons in the atom.

4. Bohr’s Atomic Model
Electrons are confined to certain orbits around the nucleus and have different energies in different orbits.
nucleus
excited states
ground state
Electrons tend to occupy the lowest energy level. This is called the ground state.
Electrons in a higher energy level are said to be in an excited state.

5. Energy Levels
Electrons can only absorb (or emit) radiation that corresponds exactly to the difference between two energy levels.
ionisation level
E0 (ground state) E1 E4 E3 E2
increasing energy
If an electron absorbs enough energy to be completely removed from the atom it is said to be in the ionisation level.

6. Learning Intentions
State that an emission line in a spectrum occurs when an electron makes a transition between an excited energy level E2 and a lower level E1
State that an absorption line in a spectrum occurs when an electron in energy level E1 absorbs radiation of energy hf and is excited to energy level E2.
Explain the occurrence of absorption lines in the spectrum of sunlight.

7. Emission Spectra
If we observe a gas (e.g. helium) through a spectrometer we can observe visible lines at the discrete frequencies which correspond with the different energy transitions for that element.
Each element has it's own unique line spectrum. This makes it possible to identify elements e.g. elements in our sun and distant stars.
The brightest lines in the spectrum correspond to the energy transitions with the most amount of electrons making that transition.

8. Emission Spectra
Emission spectra are produced when photons of radiation are emitted by electrons moving down energy levels: E0 E1 E3 E2
hf = E2 – E1
Since electrons can only occupy specific energy levels, transitions between these levels only have particular values of E. This results in line spectra.

9. Absorption Spectra
When white light such as a filament lamp is viewed through a spectrometer, a continuous spectra is viewed (all frequencies of visible light).
An absorption spectrum is produced when white light is passed through a vapour e.g. iodine vapour.
The absorption spectrum is a continuous spectrum with a series of dark lines on it. The position of the dark lines corresponds to the lines of the emission spectrum for iodine.

10. Absorption Spectra
Most of the photons from the lamp will pass through the iodine vapour. Some of the photons will be absorbed as they have just the right energy (frequency) to excite electrons in the iodine vapour to higher energy levels. This means that the frequencies corresponding to the difference between electron energy levels appear as dark lines on the spectrum.

11. Absorption Spectra
Absorption spectra are produced when electrons absorb photons of radiation and move up energy levels: E0 E1 E3 E2
hf = E1 – E0
Electrons can only absorb photons of radiation with exactly the right energy to move to a permitted energy level. This results in dark lines in a continuous spectrum.

12. Fraunhofer Lines
Absorption lines are visible in the sun’s spectrum, called Fraunhofer lines.
These absorption lines are due to gases in the sun’s atmosphere. Hence the elements present in the sun can be identified.

14. Worked Example
Calculate the frequency of the photon that is emitted when an electron moves from E3 to E0 in a hydrogen atom.
DE = E3 – E0
= (-1.36 x 10-19) – ( x 10-19)
-1.36 x J E0 E1 E3 E2
-2.42 x J
-5.42 x J
x J
= 20.4 x J
f = h DE =
6.63 x 10-34
20.4 x 10-19
= 3.08 x 1015 Hz

15. Common Questions
If asked to identify the number of possible lines for an atom we simply count the number of possible downward transitions an electron can make. e.g. for the diagram shown there are 6 possible transitions

16. Since E3-E2 is the energy transition with the smallest energy difference it will produce a photon with the smallest frequency (E2- E1=hf). This means that this photon will have the longest wavelength in the spectrum.
This means that since E3-E0 has the greatest energy difference it will emit a photon with the largest frequency and shortest wavelength.

17. Spontaneous Emission Spontaneous emission is a random process.
Spontaneous emission occurs when an electron drops to a lower energy at a time that cannot be predicted, as in radioactive decay.

18. Stimulated Emission
Stimulated emission occurs when a photon of the correct energy causes an electron in an excited state to drop to a lower energy level.
The incident photon must have the same energy, hf, as the energy transition, ∆E, undergone by the electron.
The stimulated and the stimulating photons therefore both have the same frequency. They are also in phase and travel in the same direction.

19. The Laser
A laser consists of a lasing material with mirrors on either end.
lasing material
fully reflecting mirror
partially reflecting mirror
beam
Electrons in the lasing material are ‘pumped’ to higher energy levels (e.g. by applying a high voltage). In suitable lasing materials there is a low probability of spontaneous emission.

20. The Laser (continued)
Photons that are emitted stimulate further photons to be emitted.
The mirrors on either end reflect photons back and forward and so light beam gains more energy by stimulated emission than it loses by absorption.
Laser therefore stands for Light Amplification by the Stimulated Emission of Radiation.
A parallel beam of photons is emitted through the partially reflecting mirror.

21. The Laser (continued)
Laser light is monochromatic, since all the photons have the same frequency.
The beam has a high irradiance, since all the photons are coherent and are concentrated in a small area.
Even a low power laser can cause eye damage since the power is concentrated in a very small area, giving the beam a very high irradiance.

22. Worked Example
Calculate the irradiance of light from a laser with a power of 0.2 mW. The laser produces a circular beam with a diameter of 1.5 mm.
I = A P
A = pr2
= p ( )2 =
1.77 x 10-6
0.0002
= 1.77 x 10-6 m2
= 113 Wm-2