Download Bohr awarded Nobel prize for physics in 1922

From Ideas to Implementation
When electrons (cathode rays) accelerate they produce x-rays.
Heater on anodes “boils of electrons” – electrons leave surface more easily with added heat.
Velocity Selector Crossed Magnetic and
electric fields
J.J. Thompson 1897
Crossed Field Apparatus
Anode
Cathode
x
x
X
x
x
x
x
x
x
𝐹𝑚𝑎𝑔 = 𝑞𝑣𝐵 (𝑣 = 𝑉𝑒𝑙𝑜𝑐𝑖𝑡𝑦)
Therefore when no deflection in crossed magnetic and electric fields 𝑞𝐸 = 𝑞𝑣𝐵
𝑣=
𝐸
𝐵
=
𝑉
𝑑𝐵
1
𝑠 = 𝑢𝑡 + 𝑎𝑡 2
2
By measuring deflection of cathode rays using location of ‘s ’ can be
found
1 𝑞𝐸 𝑙 2
𝑦=
( )
2𝑚 𝑣
𝑦=
1 𝑞𝑉 𝑙 2
( )
2 𝑚𝑑 𝑣
𝑞
≫ 𝐽𝐽 𝑇ℎ𝑜𝑚𝑠𝑜𝑛 1897 ≫ 𝑚 𝑐ℎ𝑎𝑟𝑔𝑒 𝑚𝑎𝑠𝑠 𝑟𝑎𝑡𝑖𝑜 𝑓𝑜𝑢𝑛𝑑 −
𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 𝑓𝑜𝑟 𝑎𝑙𝑙 𝑎𝑛𝑜𝑑𝑒 𝑐𝑎𝑡ℎ𝑜𝑑 𝑚𝑒𝑡𝑎𝑙 𝑐𝑜𝑚𝑏𝑖𝑛𝑎𝑡𝑖𝑜𝑛 −
𝑡ℎ𝑒𝑟𝑒𝑓𝑜𝑟𝑒 𝑐𝑎𝑡ℎ𝑜𝑑𝑒 𝑟𝑎𝑦𝑠 𝑤𝑒𝑟𝑒 𝑐𝑜𝑛𝑐𝑙𝑢𝑑𝑒𝑑 𝑓𝑢𝑛𝑑𝑎𝑚𝑒𝑛𝑡𝑎𝑙 𝑐𝑜𝑛𝑠𝑡𝑖𝑡𝑢𝑒𝑛𝑡𝑠 𝑜𝑓 𝑚𝑎𝑡𝑡𝑒𝑟
>> “Plum pudding” atomic model
Electrons Travelling in magnetic field
Electrons travel in the arc of a circle (not parabolic) as mag force is always
perpendicular to the motion of the electron.
Fluorescent
Paint
Mass of electron
Robert Millikon (1911?)
Apparatus floated oil drops using electric force. Oil drops became charged when sprayed.
Process:
1. Measure terminal velocity >> mass of oil drops
2. Connect plates to power supply – when drop hovers >>
𝑞𝐸 = 𝑚𝑔 where q = charge on oil drop and E = electric field strength
𝑞∆𝑣
= 𝑚𝑔
𝑑
𝑚𝑔𝑑
𝑞=
∆𝑣
Was found:
 It was found the charge for every oil drop the charge was a multiple of 1.6 × 10−19 C coulombs.
 The smallest charge found was 1.6 × 10−19 C coulombs.
Mass spectrometer
Velocity
Selector –
Crossed
magnetic
field and
electric
fields.
Voltage
used so
that 𝐹𝑒𝑙 =
𝐹𝑚𝑎𝑔
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
Ion beam
.Ion beam
in circular
arc due to
fmag
𝑣2
𝑎= 𝑟
𝑓 𝑣2
=
𝑚
𝑟
𝑞𝑣𝐵 𝑣 2
=
𝑚
𝑟
𝑞𝐵 𝑣
=
𝑚
𝑟
𝑚
𝑟
=
𝑞𝐵 𝑣
𝑞𝐵𝑟
𝑤ℎ𝑒𝑟𝑒 𝑟 = 𝑟𝑎𝑑𝑖𝑢𝑠 𝑜𝑓 𝑐𝑖𝑟𝑐𝑢𝑙𝑎𝑟 𝑝𝑎𝑡ℎ
𝑣
𝑣 = 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 𝑜𝑓 𝑖𝑜𝑛 (𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 𝑠𝑒𝑙𝑒𝑐𝑡𝑜𝑟) 𝑞 = 𝑐ℎ𝑎𝑟𝑔𝑒 𝑜𝑛 𝑖𝑜𝑛
𝑚=
Photoelectric effect
Discovered 1887 - The ejection of electrons from surface of
metal due to EM radiation
Cause
Oscillation electric field of EM wave causes electron to move >>
generates magnetic field which interacts with magnetic field of
EM wave
Facts
𝑟𝑎𝑡𝑒 𝑜𝑓 𝑒 ′ 𝑠 𝑒𝑚𝑖𝑡𝑡𝑒𝑑 𝑝𝑒𝑟 𝑠𝑒𝑐𝑜𝑛𝑑 ∝ 𝑙𝑖𝑔ℎ𝑡 𝑖𝑛𝑡𝑒𝑛𝑠𝑖𝑡𝑦
Stopping voltage = voltage just required to stop the emitted
electrons.
Generated current is called photocurrent.
Loss of KE = increase in electric PE
Electron volt
1𝑒𝑉 = 𝑒𝑛𝑒𝑟𝑔𝑦 𝑎𝑞𝑢𝑖𝑟𝑒𝑑 𝑜𝑟 𝑙𝑜𝑠𝑡 𝑏𝑦 𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑛 𝑤ℎ𝑒𝑛 𝑚𝑜𝑣𝑒𝑠 𝑡ℎ𝑟𝑜𝑢𝑔ℎ 𝑝𝑜𝑡𝑒𝑛𝑡𝑖𝑎𝑙 𝑑𝑖𝑓𝑓 𝑜𝑓 1𝑉
Photoelectric facts
1. 𝑃ℎ𝑜𝑡𝑜𝑐𝑢𝑟𝑟𝑒𝑛𝑡 ∝ 𝑏𝑟𝑖𝑔ℎ𝑡𝑛𝑒𝑠𝑠 𝑜𝑓 𝑙𝑖𝑔ℎ𝑡
𝑛(𝑒) ∝ 𝐼𝑛𝑡. (𝑝𝑟𝑜𝑣𝑖𝑑𝑒𝑑 𝑓 > 𝑓0 )
2. KE of emitted electrons is independent of intensity
3. The KE of emitted electrons depends on frequency
4. There is no emission below a threshold (𝑓0 ) regardless of intensity
5. 𝑓0 is different for each metal (its’s lowest for alkali metals / for elements with lowest ionisation energy)
6. If electrons are emitted, the emission is instantaneous
Einstein’s explanation of photoelectric effect
1. The energy of an EM wave is not spread out over the wave front. It concentrates in bundles (quanta /
photons)
2. The energy of a quantum is related to frequency of the EM wave
𝐸𝑞𝑢𝑎𝑛𝑡𝑢𝑚 = ℎ𝑓
ℎ = 𝑃𝑙𝑎𝑛𝑐𝑘 ′ 𝑠 𝐶𝑜𝑛𝑠𝑡𝑎𝑛𝑡 = 6.6 × 10−34
3. During photoemission the energy of a quatum is completely absorbed by an electron
4. In getting out of the metal some of the energy acquired by the electron is lost
𝑤 = 𝑒𝑛𝑒𝑟𝑔𝑦 𝑙𝑜𝑠𝑡 𝑜𝑛 𝑤𝑎𝑦 𝑜𝑢𝑡 = 𝑖𝑜𝑛𝑖𝑠𝑎𝑡𝑖𝑜𝑛 𝑒𝑛𝑒𝑟𝑔𝑦 (𝑤𝑜𝑟𝑘 𝑓𝑢𝑛𝑐𝑡𝑖𝑜𝑛)
𝐾𝐸𝑚𝑎𝑥 = ℎ𝑓 − 𝑤
Black body Radiation
Black body :
 Perfect absorber
 Best emitter when heater
 Stars behave like black bodies
 As temp increases >> red >> orage >> yellow >>
white >> bluish
Hertz 1887
Confirmed existence of EM waves
Wavelength was found using
interference properties. A metal plate
was used to reflect waves – created 2
waves and interference patterns.
e.g. when waves superimpose the
sparks at the collector may be twice as
big or zero
In radios f is altered by the 2 electron
delays – the size of coils and plates.
Causes other f’s to be excluded as the
current oscillates at a natural
frequency.
In normal circuits
As the switch is closed
Circuits with solenoids
I
I
t
t
The separate coils act like moving magnets as current
increases , as B increases the other coils oppose the movement of the “magnet” (due to lenses law)
SEMI-CONDUCTORS
Thermionic Devices
Were used before semiconductors – switching was slow, devices were large, used lots of electricity, ran at high
temperatures
Diode
One way conducting device – electrons flow from end as they can only escape from 1 side (due to heater)
I
t
Triode
Amplification devices – current applied to grid opposes the movement of electrons, the variations in the current are
amplified by the electrons moving through.
V
𝑉𝑚𝑖𝑐
𝑉𝑔𝑟𝑖𝑑
Silicon- an intrinsic conductor
 Is semi-conductor
 Abundant element found in sand(silicon dioxide)
 Hard to extract
 Conductivity increases and then decreases as temperature increases - due to outer shell electrons locked up
in covalent network bonds which become loose when heated
Conduction in Semi-Conductors (Intrinsic conductors)
1. Movement of freed electrons (by heat etc.)
2. Movement of “holes” (behaving as positively charge electrons – STEPWISE motion of loosely bound
electrons from atom to the left by the freed
electron)
3. Net current = freed electron + hole
current = 2 x freed electron current
4.
Doping
Silicon is irradiated to improve conductivity
03
31
𝑆𝑖14
+ 𝑛10 → 𝑆𝑖14
0
𝑛10 → 𝑝11 + 𝑒−1
31
31
0
𝑆𝑖14
→ 𝑃15
+ 𝑒−1
N- type Semi-conductor
Adding phosphorous to silicon makes N-type
semiconductor as it gives donor electrons
which are not bound in covalent bonds
Consists of:
1. Dominant donor e’s
2. Freed e’s
3. holes
P- type Semi-conductor
Made by adding boron – leaves “holes” (positive charge areas)
Consists of:
1. Dominant donor hole current
2. Free electron current
3. Freed hole current
+
--
Forward biased
reversed biased
Semi-conductor diodes
P-type stuck on to n-type
The donor e’s and holes “wander” causing + and –
charge to build up on the n and p side.
When charge is applied to forward biased direction
the depletion layer gets smaller >> increased
conductivity
When charge is applied to reversed biased
direction the depletion layer gets bigger >> lousy
conductor
Therefore >> one way conductor
+
Semi-Conductor transistors
First Invented by Bell telephone laboratories for telephone exchanges are Thermionic devices were no longer
reliable/effective (late 1940s)
AWA (Amalgamated Wireless Australia) - developed ways to use transistor
1.
2.
3.
4.
5.
Voltage at base causes depletion layer to get smaller >>
Electrons no longer repelled by negative area of depletion layer
Current flows freely from emitter to collector
Varying voltages at base allow varying levels of current through
Transistor acts as amplifier
Heavily
doped
(collector)
– reversed
biased
Lightly
doped
(base)
Heavily
doped
(emitter)
Forward
biased
Computers and Chips
Transistors are used as switches in computers
1. Big change in base voltage (on/off)
2. Collector is either on/off (1/0)
3. Acts as binary code device or Boolean gates
Why are thermionic devices still used
Vaccum triodes still used in guitar amps as sound reproduced is “Warmer” – in Transistors it is more “edgy”
Making Silicon Chips
1. Silicon wafer prepared by melting, cutting polishing etc.
2. Thin layer of oxide added by heating in oven
3. Photoresist added to surface
4. Whole thing exposed to light through a mask
5. Area hit by light hardens
6. Other areas are etched away
7. Un covered areas Irradiated (doped) with atoms (Phos. Or Boron for n or p type)
8. New layer of silicon added
9. 3-7 repeated several times
Up to 40 layers of silicon to make chips
Impact of the invention of the
transistor
Impacts:
 Allowed development of
integrated circuits
 Allowed development of
advances electronics
 computers + digital devices
are used as sources of
entertainment
 Allowed development of
computers
 Improved telecommunications
technology
Advantages:
 Allowed development of computers making lives
easier
 Improved quality of life
 Improved telecommunication
 Made life easier
 Created many jobs in Information technology and
electrical engineering
 Increased wealth of information
 Allowed storage of huge amounts of information
 Increased rate of globalisation
Disadvantages:
 Manufacture and operation of integrated circuits
requires vast amounts of energy >> enhanced
greenhouse effect + climate change + pollution
 Increasing human dependence on ∫ 𝑐𝑖𝑟𝑐𝑢𝑖𝑡𝑠
technology for livelihood and enjoyment of life
 Electronic waste >> pollution
 Huge demand for resources e.g. sand, metal, coal
++++++
--------
Photocells
1. Photon hits p-n depletion layer/junction
2. Photon gets absorbed + creates an electron/hole
pair -/+
3. Electron/hole go in opposite direction due to charges of depletion layer
+++++++++
------------
Problems / design problems with photocells
 Recombination – hole meeting electron by chance – loss of charge
 Photon may not hit depletion layer
Super conductors
When certain conductors are below Critical temperature 𝑇 < 𝑇𝑐 resistivity goes to zero
Can be cooled using liquid gases such as He and N2
1. Gas is compressed
2. Compressed gas is allowed to cool down
3. Gas expands as it is released
4. Gas particles do work
5. Gas particles lose KE
6. Gets cooler
Cryogenics = science of low temperatures
1911 – scientists succeeded in near absolute zero temperatures (0 ° K)
Type 1 superconductors
If 𝐵 > 𝐵𝑐 impossible to turn metal into superconductor no matter how low temperature
Metal
Al
Ga
Hg
In
Nb
Pb
Sn
𝑻𝒄 (𝑲)
1.176
1.083
4.153
3.408
9.26
7.193
3.722
𝑩𝒄 (𝑻)
0.0105
0.0058
0.0411
0.0281
0.1991
0.0803
0.0305
Metal
Tn
Ti
V
W
Zn
𝑻𝒄 (𝑲)
4.47
0.39
5.3
0.015
0.85
𝑩𝒄 (𝑻)
0.0829
0.010
0.1023
0.000115
0.0054
Type 2 superconductors (High temperature super conductors)
Alloys of metals or ceramics (Complex Crystal structure)
Very brittle >> hard to use
X-Ray Diffraction – Bragg’s experiment






Uses property of all EM waves – Diffraction
Designed by Bragg
Diffraction effects increase as physical dimensions of aperture approaches the wavelength of the waves i.e.
at the atomic scale
Interference from diffraction
The atomic distance can be determined by calculating the angles and the distances between the diffracted
parallel rays
𝒏𝝀 = 𝟐𝒅𝒔𝒊𝒏 𝜽 𝒘𝒉𝒆𝒓𝒆 𝝀 = 𝒘𝒂𝒗𝒆𝒍𝒆𝒏𝒈𝒕𝒉 𝒐𝒇 𝒙𝒓𝒂𝒚 𝒏 = 𝒂𝒏 𝒊𝒏𝒕𝒆𝒈𝒆𝒓 𝟏, 𝟐, 𝟑 … 𝜽 =
𝒅𝒊𝒇𝒇𝒓𝒂𝒄𝒕𝒊𝒐𝒏 𝒂𝒏𝒈𝒍𝒆 𝒊𝒏 𝒅𝒆𝒈𝒓𝒆𝒆𝒔
BCS theory of superconductivity
1. An electron passes between ion lattice, pulling ions slightly closer together >> causes increased
concentration of + charge
(if 𝑇 > 𝑇𝑐 random vibrations of lattice ions totally dominate this small effect)
2. Increased conc. of + charge attracts another electron (preventing it from colliding with lattice ions) so that
the 2nd e moves into space between the ions
3. Effectively there is a pair of electrons (copper pair) moving in the space between the lattice ions, the first
one disturbing the lattice which in turn keeps the 2nd e also moving in space between the ions
>>>> fudge >>> however only theory that can make predictions that can be experimentally verified
Max current in Super Conductor
𝐵 < 𝐵𝑐
𝐾𝐼
< 𝐵𝑐
𝑑
𝐾𝐼 < 𝑑𝐵𝐶
𝐼<
𝑑𝐵𝑐
𝐾
Current is confined to the surface of super conductors.
>> No B in the interior >> non penetration of B into superconductor >> Meissner Effect
Magnetic Levitation
Due to Meissner effect >> induced eddy currents in super C gen. fields that repel the external mag field >> eddy
currents continue until super conductor heats up
From Quanta to Quarks
Ernest Rutherford – 1871 –
1937
 New Zealand born
physicist worked with Thomson
1856-1940 at Cavendish Lab
Cambridge university
 Brilliant Experimental
physicist
 His work with alpha
particles Disproved JJ Thomsons
plum pudding atomic model
Rutherford’s Gold foil experiment – designed by Rutherford conducted by Hans Geiger and Ernest
MArsden
1. Fired alpha particles at very thin gold foil
2. Measured angles of diffraction
3. Majority of particles went straight through and some bounced back
o Passing through – meant mostly empty space
o Some bouncing back – “as incredible as if you had fired a 15 inch shell at a piece of tissue paper and
it came back and hit you” – means huge conc. of charge in a certain place
4. This contradicted the predictions of greater deflections of Thomson plum pudding model
5. Showed that atoms were mostly empty space with huge concentration of charge in nucleus
6. Were able to determine approx. size and charge of nucleus
Deductions – 79 positive charge units (79 * 1.6 * 10^-19 coulombs) >> nuclei have charges that are integral
multiples of e >>> most be particles in nucleus
Rutherford’s atomic model
Carbon 12 – Nucleus = 12 protons + 6 electrons , 6 orbiting e’s
Uranium 238 – Nucleus = 238 P’s + 146 e’s , 92 orbiting e’s
>>> was model explaining alpha and beta decay
Rutherford unhappy due to idea of e’s in nucleus
Found isotopes always differed by a P and E or more >>> Neutron????
1919 First Artificial transmutation
 Fired Alpha particles at enough H2 gas to completely stop all particles
 However scintillations were observed
 Were Proton scintillations
 Alpha collisions caused protons to fly hit screen
 Repeated with enough N2 gas to stop all particles
 Proton scintillations observed
 Conclusion >> protons were in other atoms
Speculation whether
𝐻𝑒24 + 𝑁714 → 𝑂817 + 𝑃11
𝑜𝑟
𝐻𝑒24 + 𝑁714 → 𝐶613 + 𝐻𝑒24 + 𝐻11
Not 2nd one as only 2 trails after collision in Wilson Cloud Chamber Experiment >> therefore alpha is absorbed in
collisions.
Discovery of Neutron
Adding more paraffin increased counts on Geiger counter >> in fact adding anything with lots of H+ did
Chadwick analysed the results of this experiment and concluded that the radiation was possible neutrons. By
analysing the speeds of the particles he was able to find the approximate mass of the neutron.
Nuclear force
 The positive electrons exert a huge electrical repulsion force on each other (approx. 25.6N between opp.
Protons at edge Au atom)
 However nucleus is stable
 Must be a force holding the nucleus together
 This forced called “Nuclear” force – it is short range
Binding Energy
= energy needed to pull atom apart = energy released when atom is made from its components
Energy Released
1. = (𝑡𝑜𝑡𝑎𝑙 𝑚𝑎𝑠𝑠 𝑜𝑓 𝑟𝑒𝑎𝑐𝑡𝑎𝑛𝑡𝑠 – 𝑡𝑜𝑡𝑎𝑙 𝑚𝑎𝑠𝑠 𝑜𝑓 𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑠) 𝑖𝑛 𝑘𝑖𝑙𝑜𝑔𝑟𝑎𝑚𝑠 × 𝑐 2
𝑚𝑎𝑠𝑠 𝑙𝑜𝑠𝑡 𝑎𝑠 𝑒𝑛𝑒𝑟𝑔𝑦
2. = 𝑡𝑜𝑡𝑎𝑙 𝐵𝐸 𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑠 – 𝑡𝑜𝑡𝑎𝑙 𝐵𝐸 𝑟𝑒𝑎𝑐𝑡𝑎𝑛𝑡𝑠
𝑖. 𝑒. =
Nuclear forces
In large atoms
1. Close Nucleons attracted to each other by strong nuclear force
2. However distant nucleons have less of this (e.g. ones on opposite sides of large nucleus) due to short range
of nuclear force
3. Tug of war ( local strong nuclear attracting forces VS. weaker electric repulsion )
IF a heavy nucleus is split into 2 smaller nuclei, energy would be released – as smaller nuclei have greater BE/nucleon
Nuclear reactions
144
235
239
40
𝑛10 + 𝑈92
→ 𝑈92
→ 𝑆𝑟38
+ 𝑋𝑒54
+ 2𝑛10
𝑜𝑟
92
1
→ 𝐾𝑟36
+ 𝐵𝑎141
56 + 3𝑛0
Fission products



The released neutrons go to cause other U-235 Fission causing reaction to be self-sustaining >> lots
uncontrolled fission reaction
The Fission of U-238 does not produce stray neutrons >> cannot not sustain reaction >> not as useful in
reactors or bombs.
238
239
0
239
However U-238 can be used to make Ploutonium-239 𝑛10 + 𝑈92
→ 𝑁𝑝93
+ 𝑒−1
→ 𝑃𝑢94
which fissions to
produce neutrons
Discoveries about Nuclear fission
1. Enrico Fermi (1901-1954) led the world in neutron physics.
a. Bombarded as many elements as possible with neutrons
b. When done with uranium >>> resulted in delayed emiision of beta particle >>> resulted in
production of element with high atomic number >>> first transuranic element made (transuranic
element = element with atomic number > 92)
2. Slow Neutrons are more effect that fast neutrons
a. Fermi’s co-workers (Edoardo Amaldi 1908-1989 and Bruno Pontecorvo 1913-1993) found
experiment had different results in diff. parts of room e.g. on wood table or marble – best results
with wooden talbe
b. Fermi investigate phenomenon. He put paraffin in front of neutron source >>> result massive
increased in intensity of reactions
c. Conclusion >> Slow Neutrons are better at causing fissions
d. This is because slow neutrons are unrepelled by the nucleus and spend greater time in vicinity of
nucleus >> more chance of being captured
3. Lise Meitner and Frisch Strassman Identify Fission
a. Meitner and Frisch received letter from Otto Hahn who Studied transuranics from neutron
bombardment of heavy elements >>> found barium >>> didn’t know where it came from
b. The calculated that if uranium nucleus were split the two parts would be forced apart at energies’ of
about 200 Mev
c. Meitner calculated that if the uranium nucleus were split then the mass defect of the products was
200Mev
d. Calculations confirmed fission of uranium >> explained origin of barium
4. The First observations of fission
a. Frisch returned to Copenhagen. Bombarded uranium with neutrons, emitted particles passed into
cloud chamber
b. 2 Short Fat cloud trails were observed
c. Confirmed fission reaction
Manhattan project
1. Leo Szilard idea of chain reaction sparked researched in nuclear weapons. He was sure that it was possible.
2. Approached Einstein in 1939 and urged him to write letter to President Roosevelt suggesting USA should
actively research the possibility of a nuclear bomb.
3. In 1942 US gov. made agreement to work with British government on designing and constructing nukes >>
MANHATTAN PROJECT
4. Was though there were 2 pathways to A-Bomb. Using Uranium-235 or Plutonium 239 as fuel. Unsure which
would be better the US Gov. decided to proceed with both methods
a. Uranium enrichment
i. U-234 0.006% , U-235 0.7%, U-238 99.3%
ii. Gaseous diffusion 𝑈 → 𝑈𝑂2 → 𝑈𝐹6 (𝑔) Gas Repeatedly passed through membrane filters,
the lighter + faster moving U-235 hexafluoride passes through it is a wasteful process
iii. Centrifuge technique 𝑈𝐹6 (𝑔) is spun in a centrifuge, the heavier U-238 is pushed to the
sides
238
239
0
239
b. Creating Plutonium 𝑛10 + 𝑈92
→ 𝑁𝑝93
+ 𝑒−1
→ 𝑃𝑢94
5. Developed nuclear reactors to produce plutonium for nukes - they are now mostly used for power
generation
a. Control rod (neutron absorbers) used to absorb neutrons and control reaction
b. Moderator slows neutrons to increased likelihood of fission with U-235
i. Usually small nuclei elements –
neutrons that collide with small
nuclei pass on some momentum
and slow down (whereas a large
nucleus would reflect)
ii. Originally used graphite – as
readily available, obtained and
pure HOWEVER can catch on fire
(Chernobyl)
iii. Heavy water (where the hydrogen
is deuterium) or water (Last resort)
c. Heat from coolant is piped to heat
exchanger or directly to turbine to turn
generator
Fast Reactors




Plutonium Fuel 20%
No moderator as plutonium fission best with fast neutrons
Can be made to make plutonium than it uses – U238 lines core
More risk for nuclear explosion due to lots of plutonium
Nuclear explosions from reactors
 Impossible due to lack of critical mass
 Can melt down (literally) if reaction is too fast + uncontrolled
Nuclear waste
 Can be reprocessed – chemical extraction of useful isotopes from spent fuel rods
o Not popular as dangerous and possible to make nukes
 OR Storage deep underground in geographically stable places
Spectral lines of hydrogen – Balmer’s
Equation
Was found that
1
𝜆
= 𝑅ℎ (
1
22
−
1
𝑛2
) by analysis
of spectral lines of hydrogen
𝑛 (𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑠𝑝𝑒𝑐𝑡𝑟𝑎𝑙 𝑙𝑖𝑛𝑒)
= 3,4,5,6 … 𝑎𝑛𝑑
𝑅ℎ (𝑅𝑦𝑑𝑏𝑒𝑟𝑔′ 𝑠 𝐶𝑜𝑛𝑠𝑡𝑎𝑛𝑡) = 1.0096 × 107
𝜆 = 𝑤𝑎𝑣𝑒𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑠𝑝𝑒𝑐𝑡𝑟𝑎𝑙 𝑙𝑖𝑛𝑒
1
1
𝜆
𝑚2
Furthermore = 𝑅ℎ (
1
𝑛2
∴
−
) 𝑤ℎ𝑒𝑟𝑒 𝑛 > 𝑚 and are integers
𝑓
1
1
= 𝑅ℎ ( 2 − 2 )
𝑐
𝑚
𝑛
𝑓 = 𝑐𝑅ℎ (
1
1
− 2)
2
𝑚
𝑛
1
1
𝐸𝑝ℎ𝑜𝑡𝑜𝑛 = ℎ𝑓 = ℎ𝑐𝑅ℎ ( 2 − 2 )
𝑚
𝑛
= (−
𝑤ℎ𝑒𝑟𝑒 ℎ = 𝑝𝑙𝑎𝑛𝑐𝑘𝑠 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡
ℎ𝑐𝑅ℎ
ℎ𝑐𝑅ℎ
)
−
(−
)
𝑚2
𝑛2
= 𝐸𝑛 − 𝐸𝑚 𝑚 → 𝑙𝑎𝑏𝑒𝑙 𝑓𝑜𝑟 𝑓𝑖𝑛𝑖𝑠ℎ𝑖𝑛𝑔 𝑜𝑟𝑏𝑖𝑡, 𝑛 → 𝑙𝑎𝑏𝑒𝑙 𝑓𝑜𝑟 𝑠𝑡𝑎𝑟𝑡𝑖𝑛𝑔 𝑜𝑟𝑏𝑖𝑡
∴ 𝐸𝑛𝑒𝑟𝑔𝑦 𝑜𝑓 𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑛 𝑖𝑛 𝑎 𝐻 𝐴𝑡𝑜𝑚 𝑖𝑠 𝑞𝑢𝑎𝑛𝑡𝑖𝑠𝑒𝑑
𝑖𝑜𝑛𝑖𝑠𝑎𝑡𝑖𝑜𝑛 𝑒𝑛𝑒𝑟𝑔𝑦 𝑓𝑜𝑟 ℎ𝑦𝑑𝑟𝑜𝑔𝑒𝑛 = 𝑏𝑖𝑛𝑑𝑖𝑛𝑔 𝑒𝑛𝑒𝑟𝑔𝑦 𝑓𝑜𝑟 𝐻 𝑎𝑡𝑜𝑚 = ℎ𝑐𝑅 = 13.6eV
ℎ𝑓 = (−
1
22
= ℎ𝑐𝑅(
ℎ𝑐𝑅ℎ
−
42
1
)
42
) − (−
ℎ𝑐𝑅ℎ
22
where electron
jumps from 4th to 2nd orbit
∴



Energy of electron is quantised
Orbital radius is quantised
Orbital speed is quantised
Spectra series of hydrogen
Lyman Series: m (lowest electron orbit in the
series / normal e position) = 1 n =2,3,4…∞
Balmer series: m = 2
n =3,4,5…∞
Paschen series: m = 3
n =4,5,6…∞
Brackett series: m = 4
n =5,6…∞
Pfun series: m = 5
n =6,7,8,9…∞
Classical perspective
Kinetic Energy of an electron
Centripetal force for an electron in orbit is
electrostatic attraction between nucleus
protons and the electron
∴ 𝐹𝑒𝑓𝑓 = 𝐹𝑒𝑙
𝑘𝑄𝑞
= 2
𝑑
𝑘𝑒 2
= 2
𝑟
𝐹
𝑎=
𝑚
𝑣 2 𝑘𝑒 2
= 2
𝑟
𝑟 𝑚
𝑘𝑒 2 1
𝑚𝑣 2 =
𝑟 2
1
𝑘𝑒 2
𝑚𝑣 2 =
2
2𝑟
Total energy of electron
𝑘𝑄𝑞
𝑘𝑒 2
𝐸𝑙𝑒𝑐𝑡𝑟𝑖𝑐𝑎𝑙 𝑃𝐸 = −
= −
𝑟
𝑟
𝐺𝑀𝑚
)
𝑑
2
2
𝑘𝑒
𝑘𝑒
𝑘𝑒 2
∴ 𝑡𝑜𝑡𝑎𝑙 𝑒𝑛𝑒𝑟𝑔𝑦 𝑜𝑓 𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑛 = −
+
= −
𝑟
2𝑟
2𝑟
𝑘𝑒 2
𝑡𝑜𝑡𝑎𝑙 𝑒𝑛𝑒𝑟𝑔𝑦 = −
2𝑟
ℎ𝐶𝑅 𝑘𝑒 2
𝑤 = 𝑏𝑖𝑛𝑑𝑖𝑛𝑔 𝑒𝑛𝑒𝑟𝑔𝑦 = 2 =
𝑛
2𝑟
(𝑏𝑦 𝑎𝑛𝑎𝑙𝑜𝑔𝑦 𝑜𝑓 𝑔𝑟𝑎𝑣𝑖𝑡𝑎𝑡𝑖𝑜𝑛𝑎𝑙 𝑃𝐸 = −
𝑟=
𝑘𝑒 2
2𝑊
2𝑊
𝑉=√
𝑚
Orbit period
2𝜋𝑟
(𝑜𝑟𝑏𝑖𝑡 𝑡𝑖𝑚𝑒)
𝑇=
𝑣
3
1
𝑣
2 𝑤2
𝑓= =
=√
𝑇 2𝜋𝑟
m . 𝜋𝑘𝑒 2
)
Bohr’s Model of the atom
Bohr awarded Nobel prize for physics in 1922
Bohr’s Postulates
1. Electrons in an atom exist in “stationary states” in which they possess unexplainable stability. Any
permanent change in their motion must consist of a complete transition from one stationary state to
another
2. In contradiction to classical ERM theory, no radiation is emitted from an atom in a stationary state. A
transition between 2 stationary states will be accompanied by emission or absorption of EM radiation (a
photon). The frequency of the photon is given by: ℎ𝑓 = 𝐸1 − 𝐸2 𝑤ℎ𝑒𝑟𝑒 𝐸1 = 𝑒𝑛𝑒𝑟𝑔𝑦 𝑜𝑓 𝑖𝑛𝑖𝑡𝑎𝑙 𝑠𝑡𝑎𝑡𝑒 𝐸2 =
𝑓𝑖𝑛𝑎𝑙 𝑠𝑡𝑎𝑡𝑒
Bohr’s explanation of apparent classical nature of electron orbits
Bohn said the Bumpiness (quantised nature) is not noticed in the shorter wavelengths (high transitional f’s) because
the electron orbits are very close together.
ℎ𝑖𝑔ℎ 𝑡𝑟𝑎𝑛𝑠𝑖𝑡𝑖𝑜𝑛𝑎𝑙 𝑓 (𝐵𝑜ℎ𝑟)
1
1
𝑓 = 𝑐𝑅 (
− 2 ) 𝑓𝑜𝑟 𝑡𝑟𝑎𝑛𝑠𝑖𝑡𝑖𝑜𝑛𝑠 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑜𝑟𝑏𝑖𝑡𝑠
2
(𝑛 − 1)
𝑛
= 𝑐𝑅(
2𝑛 − 1
)
(𝑛 − 1)2 𝑛2
≈ 𝑐𝑅 (
𝑓=
2𝑛
) 𝑎𝑠 𝑛 → ∞ =
𝑛 2 𝑛2
2𝑐𝑅
𝑎𝑠 𝑛 → ∞
𝑛3
𝐸𝑞𝑢𝑎𝑡𝑖𝑛𝑔 𝑐𝑙𝑎𝑠𝑠𝑖𝑐𝑎𝑙 𝑓 𝑎𝑛𝑑 ℎ𝑖𝑔ℎ 𝑡𝑟𝑎𝑛𝑠𝑖𝑠𝑡𝑖𝑜𝑛𝑎𝑙 𝑓 (𝑏𝑜ℎ𝑟)
3
3
2cR
2
√
=
n3
m
𝑤2
.
𝜋𝑘𝑒2
𝑘𝑐𝑅
2
2 ( 𝑛2 )
√
=
.
m 𝜋𝑘𝑒2
2
𝑟𝑒𝑠𝑢𝑙𝑡 𝑤ℎ𝑒𝑛 𝑠𝑞𝑢𝑎𝑟𝑒𝑖𝑛𝑔 𝑏𝑜𝑡ℎ 𝑠𝑖𝑑𝑒𝑠 ≫> 𝑅 =
Quantisation of orbits
𝑘𝑒 2
𝑘𝑒 2 𝑛2
ℎ𝑐𝑅
(𝑐𝑙𝑎𝑠𝑠𝑖𝑐𝑎𝑙) =
𝑟=
.
𝑠𝑖𝑛𝑐𝑒 𝑊(𝑖𝑜𝑛𝑖𝑠𝑎𝑡𝑖𝑜𝑛 𝑒𝑛𝑒𝑟𝑔𝑦 𝑶𝑹 𝑤𝑜𝑟𝑘 𝑓𝑢𝑛𝑐𝑡𝑖𝑜𝑛) = 2
2𝑊
2 ℎ𝑐𝑅
𝑛
𝑘𝑒 2
∴ 𝑟 = 𝑛2 [
] (𝑛 = 1,2,3,4 … . . )
2𝐻𝑐𝑅
≫> 𝑟𝑎𝑑𝑖𝑖 𝑜𝑓 𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑛 𝑜𝑟𝑏𝑖𝑡𝑠 𝑖𝑠 𝑞𝑢𝑎𝑛𝑡𝑖𝑠𝑒𝑑
𝑟𝑛 =
2 4
2𝜋 𝑚𝑘 𝑒
𝑛2 ℎ2
4𝜋 2 𝑚𝑒 𝑘𝑞𝑒2
Quantisation of angular momentum
2𝑊
2 ℎ𝑐𝑅
(𝑐𝑙𝑎𝑠𝑠𝑖𝑐𝑎𝑙) = √ . 2 (𝑖𝑛𝑡𝑒𝑟𝑔𝑟𝑎𝑡𝑖𝑛𝑔 𝑞𝑢𝑎𝑛𝑡𝑢𝑚 𝑡ℎ𝑒𝑜𝑟𝑦)
𝑉=√
𝑚
𝑚 𝑛
ℎ3 𝑐
2 ℎ𝑐 2𝜋 2 𝑚𝑘 2 𝑒 4
2𝜋 2 𝑚𝑘 2 𝑒 4
= √ . 2.
𝑠𝑖𝑛𝑐𝑒
𝑅
=
𝑚 𝑛
ℎ3 𝑐
ℎ3 𝑐
𝑣=
2𝜋𝑘𝑒 2 1
.
ℎ
𝑛
2𝜋𝑘𝑒 2 1
ℎ2
𝑚×𝑣×𝑟 = 𝑚.
. . 2
. 𝑛2
ℎ
𝑛 4𝜋 𝑚𝑘𝑒 2
∴ 𝑚𝑣𝑟 = 𝑛.
ℎ
≫≫ 𝑎𝑛𝑔𝑢𝑙𝑎𝑟 𝑚𝑜𝑚𝑒𝑛𝑡𝑢𝑚 𝑖𝑠 𝑐𝑜𝑛𝑠𝑒𝑟𝑣𝑒𝑑
2𝜋
Limitations of Bohr’s atomic model
 Only works for hydrogen (impossible to calculate the wavelengths of spectral lines of all other atoms)
 Works well for atoms with one electron in outer shell but not when there are more
 Bohr model does not explain why some electron transitions why some electron transitions are favoured (i.e.
can’t explain why spectral lines are brighter)
 Careful observations with better instruments showed other lines (known as hyperfine lines) – there must be
some splitting of energy levels that Bohr model can’t explain
 When gas is excited in magnetic field emission spectral lines are split (called Zeeman effect) – Bohr model
cannot account for this
 Bohr model is a mixture of classical and quantum physics – this is a problem. i.e. semi-classical >> not a true
quantum theory
Momentum of photons
 Compton (US scientists) fired EM at electron clouds in 1923.
 Found most electrons absorbed the EM gained energy and flew off
 However at X-rays and above after collision the electron flies off and other photons are emitted at lower
frequencies
ℎ𝑐
𝜆
ℎ
𝜆

Thought that 𝑚𝑐 2 = 𝑝. 𝑐 =



Measured the energies of the scattered waves to test this idea
Found to be true
Conclusion >> photons with big p act more like particles
∴ 𝑝𝑝ℎ𝑜𝑡𝑜𝑛 =
Louis De Broglie 1924
 Suggested that particles have wave properties
 Said “…if something that we normally think of having wave properties can,
under some circumstances be thought of having particle properties” (e.g.
em wavres >> photons)“ then perhaps things that we normally think of
being particles can under some circumstances have wave characteristics”
(electrons >> as waves)
 His achievement was that he developed this idea mathematically
 Suggested that the quantised nature and the stability seen in the Bohr
Model was due to the “matter wavelength” of the electrons and the
relationships 𝑛𝜆 = 2𝜋𝑟 and 𝜆 =
ℎ
𝑚𝑣
De Broglie “standing wave” pattern
where λ = wavelength of electron and m = electron mass and n = integer
Evidence of De Broglie theory – Davisson and Germer Experiement 1927
 Fired electrons at rotating Nickel Crystals
 Expected to go in random directions
 HOWEVER the direction of the scattered electrons coincided with the predictions of Bragg’s law which is
usually applied to X-Rays






Furthermore they calculated the wavelength to be one feined by De broglie’s formula
G.P. Thomson (JJ’s son) tried with gold foils – found interference patterns and diffraction
CONCLUSION >> electrons have a wave properties
PROBLEM >> WTF IS AN ELECTRON?
SO what >> used whatever theories (wave or matter) to solve problems
>>> Troubled Einstein