# Quantum Mechanics

OCR A specification. Everything you need to know. written for dummies by a dummy! :D

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• Created by: Jenna k
• Created on: 11-04-14 07:22

## Energy of a photon

Electromagnetic radation was thought just to be a beam of energy until photons were discovered and it was discovered that electromagnetic reation is just a wave, a stream of these tiny photons. So you need to know that electromagnetic radtiation (waves) are just streams of photons (energy packets).

You need to state that a photon is a quantum of energy of electromagnectic radiation. Meaing the quantiy of energy that is proportional in magnitude to the frequence of the radiation.

Findinf the energy of a photon is crusial to the last statement so you need to know how to work it out. It is given by an equation E=hf. E is energy of the photon, F is the fequency associated with the photon and h is Plancks constant. (Plancks constant is 6.63x10^-34J. This should be given to you in the formula booklet.) Equally it is also given by E=hf/ Lambda. (Lambda being wavelength)

Once you have calculated the energy of a photon you will find that your answers are in Joules. This is due to the electron volt. (eV). We know that 1 V equivelant to JC^-1. And we know that e is the elermentary charge of an electron. So we get the equation JC^-1 x 1.6x10^-19 C. The coulomb units cancel as one is 1/C and the other is C leaving the units of joules J. You dont need to be able to spout this out, but if you come across a question you need to be able to remeber that the Coulombs cancel and the eV is measured in Joules not Volts or anything else.

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## Evaluation of Plancks constant

This is slightly trickier than the previouse page. To find, and therefore evaluate, Plancks constant you need to use LED's.

When LED's emits light caused by electron flowing through the component (Think back to DC curcits) As each electron passes through the LED, an fixed amount of of energy is lost. The enrgy lost is linked to the photons energy. This is given by the equation:

Energy lost by electron = charge on the electron X potential differance across the LED.

This should remind you of eV. So energy lost by the electron =eV.

From this we can combine two equations to get eV = hf

We already know the frequency of the LED, as it will be provided on the packet of the LED's. Thus we now know e and V and f so we can work out h (Plancks constant).

Alternatively there is another equation you could use if you had wave length.

It is eV =hc/lambda.

The only new things here are c and lambda. You should know the c is the symbole of the speed of light which will be in you formula booklet, but it is 299 792 458 ms^-1. So you have two constants (e and c) one that will be given to you (lambda) and two you can find out ( V and h)

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## Photoelectric effect

This is really cool!

An electroscope is set up. This has a stem that is negitiveky charged. Attached to the stem is a peice of gold leaf which is also negitively charged, so they both repel each other. When a peice of Zinc metal is place on the top. When UV light is shone on it the gold leaf moved toward the stem of the electroscope. This is becasue the UV light removes electrons form the zinc thus causing the charge of the stem to change slightly to attract the gold leafe a bit. The interesting thing it that when the UV light is removed, the gold leaf does not return to its origonal position but just stops. This shows that the electrons emited form the Zinc are well and truely gone. The name of this effect is photoelectric because the electrons emited for the Zinc are called photoelectrons hence the name.

This photoelectric effect is proof for the particular nature of electromagnetic radiation, as the photoelectrons were emited from the Zinc one by one in the presence of the UV light. Thus there must be particles in the UV that are "bumbing" the photoelectrons off of the Zincs surface.

However we know that electromagnetic radiation can be diffracted and interfered with prove that electromagnetic radiation has a wave nature as well as a particulate nature.

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## Photoelectric effect continued

Intensity affects the energy of photoelectrons. We have learnt that the energy of a wave is proprotional to its intensity, so when the UV is removed the Kenetic energy reduces too. But this is not the case.

When the intesity of the UV light was low the maximum concestic energy remaind constants. This means that number of photoelectrons decrease bu the the photoelectros still moving had the maximum movement.

Einstein reseached this is depth and even won a nobal prize for it. He suggesed that the UV quantum of energy (hf) hitting the metal plate was used to release an electron form a surace atom. Any energy remaining was used as kenetic energy of the electron. This is conservation of energy. If the energy is not used then it is converted and used in a different way.         The equation to reprosent this is Photon energy = energy to relese electron + keneti energy of an electron.

hf = work function energy +(1/2 x mv^2)max

This maximum kenetic energy is hard to get your head around. But it is when the UV light reduces the negitive charge of the plate, by forcing particle (photons) into the metal. This knocks electrons that are closest to the exterior of the atom out of obit. This knocking is a trasferal of energy, which is converted into kenetic energy. If there is maximum kenetic energy that means that on its path way for the atom of origon it does not get hit again and its course is not changed. If it did get hit by another particle then it is not included in the maxium kenetic energy of the particels. This makes sense becasue the wavelength and frequesnce of the UV light  and the maxerial is always the same. So there will never be more electrons or photons. However if you increase the the intesity there will be more collision between the obrital electrons. However there will also be more collisions betwenn non-orbiting electrons and photons. So that is why the kenetic energy is alway the same in the photoelectric effects.

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## Photoelectronic effect: one last thing

That equation we was talking about previousely  (hf = work function energy +(1/2 x mv^2)max) looks like y=mx+c when rearaged. hf - work function energy =(1/2 x mv^2)max. If h is the gradient, f is the x value and Kenetic energy is the y valaue. This on a graph would look like->

This shows the thresholf frequency where the line crosses the x axis. This only occures with metals in the UV light part of the spectrum. This means that the UV light has enough energy to release photoelectrons from the surface of the metal.

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## Wave-particle Duality

This is a very posh way of says the electromagnetic radiation acts as a wave and as a particle. Which I have talked about before.

Just before we start, I want to tell you baout the history of this pronciple. Mr. Compton stated that x rays were coliding with electron and behaving as particles. Thus reinforceing that idea that electromagnetic waves could be condiered as a stream of particles (photons)

Then Mr. De Broglie ( De Broy) then suggested that Electromagnetic waves actually act as both. He then went on to proved this which is what I'm going to explain below.

Electron diffraction is eveidance for the wave like nature of paritcle like electrons. De Broglie set up a electron gun which accelerated electrons through a valuccum towards a layer of polycrystillein graphite since using a diffraction gradient is not suitable. When seen on a bark background a circular patturn was exhibited. It looked like a white dot in the middle and then slowly diming bands that followed outwards. Lokk it up it is cool!

From this you need to be able to measure the wavelegth. This is simply done by measureing the ring diaminters in a diffraction pattern. The wavelegth is inversely proportional to the spped of the electoron. Thus the election wavelength = h / mv m being mass v being speed and h being Plancks constant.

The practical applications of the electron diffusion is that we can determine the atomic spaceing of a material and the structrue of the matter and the arragement of the atoms in a crystillled sturcture.

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## Spectra

Joseph Von Frauhfer suggested that when looking at spectrums each element produced as unique pattern.

Line spectra is produced by hot gases. This is just a spetrum with some balck lines on it at specific wavelengths. The black lines reprosent the elerments in the atomospher of that Sun, Plante of something 'gassy' (It was'nt me!) . As there is an absorbtion spectra, which works in hand wiht the linear spectra. This just suggests that the black lines are the wavelengths of light that are being absorbed by the different elerments in the atmospher of the object.

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## Energy levels in atoms

Now we going to talk about Bohr. No not the man who did Bohr shift in haemoglobin.

Simplely put he said that atoms dont have orbitals or shells that are ridged and had specific amoutns of electrons on them. He siad that there are levels that each electron can exist on. These are not fixed and eletrons can move between the the energy levels.

When electrons move twoeard the nucleous there is raditaion that is admited. This is becasue the elctron moves from a higher energy level to a lower energy level thus releasing spare nerfy as radiation.

This is shown as hf = E1 - E2 where E1 is associated with the energy level the electon has left and E2 being the energy associated with the level that the electron has moved to.

This can also be writen as hf/ lambda = E1 - E2

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