 # 03 Quantum Phen Mob Rev

Use these quick notes to help you revise each topic from the Chapter.

3.1 Photoelectricity

Discovery of Photoelectricity

• In 1887, the German physicist Heinrich Rudolf Hertz discovered an interesting property of matter.
• This property is that physical materials emit charged particles when they absorb radiant energy (eg, light). Of course, not all substances absorb radiant energy, and the ones that don’t will not emit charged particles.
• Hertz initially observed that the minimum voltage required to draw sparks from a pair of metallic electrodes was reduced when they were bathed in ultraviolet (UV) light, such as from a mercury vapour lamp. The more intense the UV light, the lower the required voltage became.
• This was later named the “Photoelectric effect”

Electromagnetic Radiation travels at the speed of light in a vacuum or 3.00 x 108ms-1. EM radiation has many forms and there is a “spectrum” of radiation which under the wave model propagates (moves) through space with both frequency and wavelength.

c = fλ

We find that the spectrum has various interactions with matter and can be quite dangerous when l is short i.e. gamma rays.

Visible Light

The energy E, frequency f, and wavelength λ of a photon are related by the formula;

E =hf

= hc/λ

where h is Planck’s constant and c is the speed of light. For example, the spectrum of visible light consists of wavelengths ranging from 400 nm to 700 nm. (1nm = 1 x 10-9m) Photons of visible light therefore have energies ranging from

Emin =1.78 eV    to   Emax = 3.11 eV

An electronvolt is also the energy of an infrared photon with a wavelength of approximately 1240 nm. Similarly, 10eV would correspond to ultraviolet of wavelength 124 nm, and so on……

Photoelectricity

The idea of this is simple, when we shine a UV light source on a gold leaf electroscope which is charged negative (i.e. has lots of electrons) we find that the leaf falls. The conclusion is that electrons escape from the surface. This happens differently for different metals and different light sources.

Photoelectricity – effect of frequency

When you change the frequency of light incident on the surface the energy radiant on the surface per photon or E = hf increases or decreases. This means that the energy of the electron emitted changes (increase or decrease). If you fall below a threshold frequency you don’t have enough energy to emit a photon and it does not happen.

Photoelectricity – intensity

If you change the number of incident photons i.e. the light colour is the same but the intensity or number arriving per second goes up. The number of electrons emitted goes up.

Photoelectricity – formula

So if we consider we input some light energy to the surface (hf), then take away the work done to get the electron to the surface (f), then the electron leaves with the leftovers (EKmax)..

EKmax = hf – φ

Plotting a graph of this as EKmax– Y   & f – X leaves “h” as the gradient which is always a constant no matter which surface and “φ” – the work function or energy to get to the surface!

Photoelectricity – Threshold

If you consider the situation where the line graph EKmax = hf – φcrosses the X axis this is when EKmax =0, Hence we can say that 0= hf0φ  or that f0 = φ/h . This is called the “threshold frequency.

Photoelectric Marking Summary

• Light incident on a surface has energy hf (changes on colour due to f)
• Electrons are emitted with various KE’s up to a maximum which depends on f
• Each surface has a “work function” φ which is the energy absorbed by the surface from the initial photon.
• Effect is instant
• One photon has to be absorbed by one electron so no build up effects (tells us it is a quantum effect  10-9S)
• More photons in (more intense) gives more electrons (not higher EKmax.
• There is a threshold frequency so if the initial frequency is not high enough then effect does not happen.

3.2 More on Photoelectricity

Planck’s Model

Plank suggested that energy could be thought of a discrete values instead of a continuous scale. Where things only happened when the correct energy value was added. He thought of atoms as having energy shells where electrons could be moved up a level by absorbing energy E = hf. This is why the photoelectric effect uses the idea of E = hf as it behaves in a quantum way instead of a wavelike way.

Conduction Electrons

Electrons in a metal move about as a disassociated sea. They can be given energy to form an electrical current but they have to have a large amount of energy per electron to be removed from the surface. This can be provided by the light when E = hf is high enough.

Vacuum Photocell

The whole experiment  for photoelectricity can be more accurately completed with a cell which has a cathode, anode and microammeter in a vacuum tube. Light is incident on the cathode and electrons escape. We can use the ammeter current to show the effect of the electrons escaping and draw the graph of….

EKmax = hf – φ

This shows EKmax– Y   & f – X leaves “h” as the gradient which is always a constant no matter which surface and f – the “work function” or energy to get to the surface!

Photo electricity – Models

Try this analogy, which involves ping-pong balls, a bullet and a coconut shy. An elderly lady tries to dislodge a coconut by throwing a ping-pong ball at it – no luck, the ping-pong ball has too little energy!

She then tries a whole bowl of ping-pong balls but the coconut still stays put! Along comes a physicist with a pistol (and an understanding of the photoelectric effect), who fires one bullet at the coconut – it is instantaneously knocked off its support.

This is the idea of one photon in -> electron out.

Also a nice one I thought of is protesters and police. The police drag out the protesters one by one.  Then higher energy police officers come along and drag out the hardcore protesters with more force. You have compare violet light to UV (or ultra-violent!)

Energy Levels in Atoms 3.3-3.5

Orbital Electrons

These are electrons which orbit the atom in fixed energy shells. They can be in what is called the ground state – the lowest energy level. But if atoms absorb energy i.e. E = hf from photon or electron collision then they can move to what is called an excited state.

Ground State & Ionisation

Lowest energy state for an orbital electron. For hydrogen it is -13.6eV/n2. What this means is I have put in 13.6eV or 8.16 x 10-19J of energy to remove that electron from the atom. This is also called “ionisation” and would make the hydrogen atom a lone proton.

Excitation or De-excitation (Photon)

This is when a photon E = hf of exactly the right energy is absorbed into an atom making an electron move 1 or more shells further out. The reverse process is de-excitation.

Fluorescence & Tubes

The atoms of a fluorescent substance may get excited by incident uv light. We can coat a glass evacuated tube with this substance so then these atoms then de-excite emitting visible light. This is a method of converting UV light to visible which we can use.

These tubes cannot operate at normal voltages to start with as resistance of the gas inside is too much. However this can be overcome with a starter circuit.

• In the Starter (a time delay switch):  an electric current warms the filament electrodes.
• During the first second argon vapor in the starter conducts and warms up a bimetallic
• strip which bends and switches off  the current flowing through the  filament electrodes.
• The mains voltage then acts across the filament electrodes causing the gas to glow.

Low Energy Bulbs

Most light bulbs waste most energy as heat. However, a high efficiency fluorescent tube is much more efficient and can also be run at a lower input power as well. This is better for the environment.

Efficiency = (useful energy out / total energy ) x 100%

Geissler Tubes

The tube was invented by the German physicist and glassblower Heinrich Geissler in 1857. It consists of a sealed, partially evacuated glass cylinder of various shapes with a metal electrode at each end which contains rarefied gasses such as neon, argon, or air; mercury vapor When a high voltage is applied between the electrodes, an electrical current flows through the tube. The current disassociates electrons from the gas molecules, creating ions, and when the electrons recombine with the ions, the gas emits light. The light emitted is characteristic of the material within the tube, and is composed of one or more narrow spectral lines.

Excitation from Collision

When a high energy electron collides with an orbital electron if it has more energy than a shell jump it can excite the electron leaving any spare energy with the incoming electron to leave with that as its kinetic energy.

Energy levels Formula.

We find that we can work out the energy difference simply by the formula..

E = hf

= E2– E1

= hc/λ

= (-13.6eV/n22 – 13.6eV/n12)

We use the ground state of hydrogen as -13.6eV but for other atoms it would change. The n = 1,2,3,…. is the shell number.

-13.6eV/n2

3.6 Wave-Particle Duality

De-Broglie Hypothesis

This was an idea that all matter in fact has a wavelength just like light…

λ = h/mv  = h/p

(p is momentum, v = velocity, m = mass)

However, for everyday items such as tennis balls when they are hit at high speed the wavelength is very small as not to be noticed. This is not the case for the electron.

Also he said that electrons can form standing waves in orbit around an atom. The number of wavelengths relate to the shell number i.e. λn where n is the shell number.

Dual Nature of Light

• The photo electric effect provides evidence of light being particle-like in nature
• The diffraction of light provides evidence of light being wavelike in nature

Dual Nature of Matter

•  Evidence of matter being wavelike in nature  ( also electron deflection in electric and magnetic fields)
• The diffraction of an electron beam directed at a thin metal film provides
• The rows of atoms in the metal crystals behave like light passing through slits for it to happen should be λ similar to size of atoms.

Electron waves and Ring size

Speed of electrons effects the size of rings…

• Higher Anode Voltage = Faster Electrons
• Diffraction Rings are smaller
• The wavelength λ is smaller

λ = h/mv  = h/p

(p is momentum, v = velocity, m = mass)

TEM

Is a transmission electron microscope where electrons are accelerated to a high speed to produce a very short de Broglie wavelength. Very detailed images can then be resolved

MRI

Magnetic resonance imaging is when radio waves are emitted when hydrogen nuclei ( eg in water molecules) change energy states in a strong magnetic field.

STM

A scanning tunnelling microscope can map surfaces using a quantum tunnelling effect where the a small tip is very close to surface.

SQUID

superconducting quantum interference device – magnetic field detector

Used to detect very weak magnetic fields from tiny electrical currents inside the brain  and for feotal examinations.