# Photons

2.3.1 The Photoelectric E ect
Charging an electroscope:
1. Bring a negatively charged rod, close to, but not touching the top plate
2. The negative charge of the rod will repel negatively charged electrons in the top which will move into the gold foil. This is charging by induction

3. The top plate has a lack of electrons, so when earthed by a nger, it gains electrons
4. Removing the earth connection and rod leaves an overall excess of electrons and so the electroscope is negatively charged
In order to investigate the nature of light and how much energy is associated with it, some scientists set up an electroscope and tried to discharge it with red light (∼ λ = 650nm) but the plate never discharged. They then repeated the procedure but with UV light, and found that it discharged immediately, but slower for a less intense source. Light could not have been acting like a wave when in the red light’s case, or the electroscope would have to discharge at some point. So it was soon found that light was acting as a particle, known as photon. The energy of that photon can be calculated from:

2.3.2 Stopping Voltages
If the frequency of a wave and the work function of a material is known, you can calculate Ekmax using Einstein’s Photoelectric e ect equation, and these values can be found experimentally using a stopping voltage experiment. Experimental method:
1. Shine monochromatic radiation onto a photocell with V set to zero

2. Check the ammeter, if it is reading is zero, then the photon energy is less than the work function
3. Increase the frequency until current is measured, and when current appears, f = f0
4. Increase frequency and so the current will rise, so then increase the voltage opposing the current, and just as it reaches zero, record the voltage required and the frequency and the voltage can later be converted to Ekmax using eV
5. Plot a graph of the results, the y-axis will be recorded as Ekmax and the x-axis as the f which will mean that the gradient is a constant h and the y intercept while not being `real’ (since there are no `negative’ frequencies to produce a negative Ekmax), if you extend the line to nd it, it will be negative the work function

2.3.3 X-Rays
X-Rays are a part of the electromagnetic spectrum that can be used to see inside the body to check bones for fractures, they allow us to see the bones, because they penetrate skin and other tissues, but they cannot penetrate bones. XRays are produced when high-speed electrons decelerate quickly. Highenergy X-rays have shorter wavelengths than low-energy gamma rays, so it is impossible to tell them apart, they are only given di erent names

because of the way they are produced. X-rays can be produced in a specialized vacuum tube, known as an X-ray tube. Like all vacuum tubes, there is a cathode which emits electrons into the vacuum and an anode to collect the electrons which sets up a ow of electrical current, known as a beam, through the tube. A high voltage (30−150kV for example) power source is connected to the cathode which accelerated the electrons towards the anode material which is usually tungsten, molybdenum or copper. The high voltage accelerates the electrons through a large potential di erence, and most of this energy is simply released at the anode, but on rare occasions, the electrons can excite electrons in the anode and cause them to emit X-rays when they lose this energy and spontaneously emit X-rays (about 1% of the energy is released as X-rays, and the photons are usually emitted perpendicular to the path of the electron beam). The cathode is usually a heated lament in modern machines, and the anode is a disc attached to a motor which rotates it to prevent it from melting and a cool oil bath absorbs remaining heat. A lead shield is used to surround the device to prevent X-rays from escaping in all directions. The X-ray spectrum produced depends on the anode material and accelerating voltage. In many applications current ow is pulsed on for between 1ms and 1s which enables consistent doses of X-rays. This graph shows intensity against wavelength of the energy emitted.

2.3.4 Electromagnetic Spectrum
Radio waves have the greatest amount of energy, and it falls through the spectrum until gamma rays which have the least amount of energy in the spectrum. Radio waves are used for television (digital and analogue) and radio (FM, AM and MW). Microwaves are used in microwave ovens for cooking, GPS (Global Positioning System) for location via satellites and for mobile phone networking. Infrared is a form of radiation that we feel as heat, it is used in night-vision cameras, and in remote controls. UV is used to sterilise water, purify air, and for security/forensic purposes. X-rays are used in medical scans to check bones

for breaks and fractures. Gamma rays are used in radiotherapy to kill cancers, however they also cause cancer, so they must be used in carefully controlled doses

2.3.5 Line Spectra and Absorption Spectra
Continuous spectra are ones where all visible wavelengths of light are present. `Filtered’ spectra is a continuous spectrum, but over a limited range, part of the spectrum has been absorbed. Line spectra are ones that contain only a few wavelengths, energy can be spread di erently to wavelengths which can cause one colour to dominate, and line spectra are always formed by atoms which have been excited. Monochromatic spectra are ones which contain only one colour caused by a high concentration of energy in similar wavelengths. Excitation is the process of giving an electron in an atom more energy which causes it change energy state. If an electron is moved to an energy level higher than the ground state, it will normally de-excite very quickly. An atom can be excited by either electron collision or photon absorption, in the case of an electron collision, the amount of energy does not have to match the speci c energy gap, but a photon absorption does. When an electron de-excites, it will release a photon of the same energy quantity as the gap. The formula for de-excitation:
E2 −E1 = hf

2.3.6 Stimulated Emission
When a photon is emitted by a stimulated emission (which is photons are used stimulate an electron to `fall’ down an energy level releasing a photon), the light emitted is coherent to the input photons.
2.3.7 Population Inversion
Population inversion occurs when a system (i.e. a group of atoms or molecules) is in a state where more electrons are in an excited state than in lower energy states. The number of atoms in the ground state is notated as N1 and the number in the excited state is notated as N2 and the total number as N. So when

population inversion occurs, N2 > N1. Population inversion is not (usually) possible with a two-level energy system because de-excitation will occur to fast.
2.3.8 Three-level Lasers
Population inversion can however, be generated in three-level energy systems. We must consider three energy levels, notated E1, E2, E3, where E1 is the ground state and three populations of respective energy levels, notated N1, N2, N3. Initially, all electrons will be in E1 (ground state), but if we then provide electrons with energy using a process called pumping, they will be excited to E3, such that N3 > 0. Pumping can happen due to excitation from light, electrical discharge or chemical reactions. The electrons in E3 then `move’ down to E2, `move’, because electrons do not actually move between energy levels, they quantum tunnel, which is the name given to the process of donating matter to the vacuum before appearing somewhere else. such that N2 > 0 and while it should release an electron, in practice usually it doesn’t but passes the energy to the body as kinetic energy. The electrons then `move’ down to E1 but if it takes longer for electrons to `move’ from E2 to E1 than E3 to E2, than the population of E3 will be e ectively zero (N3 ≈ 0) and electrons will accumulate in E2 (the metastable energy level), such that a population inversion can be achieved where N2 > N1. The population inversion causes a large number of photons to be emitted. Photons of the correct wavelength are put into the system to ensure that the light emitted is coherent, this is because these photons cause the electrons to release photons through stimulated emission rather than spontaneous emission. The material being lased is then trapped in-between two mirrors which cause the photons to stimulate further electrons which causes yet more photon emission and because one of the mirror is only partially silvered, you can access that light energy. Threelevel lasers are ine cient compared to four-level and others, because they must be very strongly `pumped’ to work (this is because of the input photons for stimulated emission, see four-level lasers below), however, both are extremely ine cient in general (< 1%, usually around 0.01%).

2.3.9 Four-level Lasers
Four-level lasers are very similar to three-level lasers, but they generate population inversion slightly di erently when `pumped’ because they have four energy levels. There are four energy levels, E1 (ground state), E2, E3, and E4 and four

respective populations N1, N2, N3 and N4. You must rst excite the electrons to E4 (via pumping). The electrons then `moves’ down down E3 with a fast radiation-less transition (much like in three-level lasers). The electrons accumulate in E3 because it is metastable, and as such, population inversion occurs and so the electrons release photons by stimulated emission caused by input photons. The last change from E2 to E1 is similar to that from E4 to E3 with no radiation. Three level lasers can be ine cient, because photons fed into the system to cause stimulated emission (rather than spontaneous emission), can also excite electrons in the ground state (where electrons often accumulate) and as such, four-level lasers are much more e cient, because the photons cannot excite ground state electrons to the E3, only from E2 to E3 which is much less likely because E2 is usually empty because it is not metastable.

2.3.10 Semiconductor Diode Lasers
Semiconductor diode lasers (also known as laser diodes) are lasers where the medium is a semiconductor. The diode is created by doping the surface of the semiconductor (normally an alloy of aluminium and gallium arsenide) with a very thin layer on the surface and the doping produces a n-type and p-type region one above the other. Electron are injected into the diode’s `holes’ and some of the excess energy is converted into photons, which interact with more incoming electrons producing more photons. Just like in a conventional laser, the electrons are `pumped’, but in a laser diode, this happens in the tiny (∼ 1µm) junction (which is known as the Fabry-Perot resonant cavity) between the slides of p-type and n-type semiconductor.

2.3.11 Advantages and Uses of Semiconductor Lasers
Semiconductor lasers are better than other laser for many uses because they are small, cheap, e cient and more versatile, but they provide worse optics because regular lases don’t require external optics, while a semiconductor laser do. Semiconductor lasers are used in telecommunication, bre optics, barcode readers, laser pointers, CD, DVD & Blu-ray technology, and laser printers.