Modern Physics

By

Neil Bronks

Atoms

C12

6

Mass Number - Number of protons + Neutrons.

Atomic Number - Number of protons

In a neutral atom the number of electrons and protons are the same. In Carbon it is……… 6

Hydrogen

Electron

Proton

The simplest atom has one negative electron orbiting one positive proton.

The electron is very light compared to the proton.

Helium

Neutron

In this atom we see two neutrons and two protons forming the nucleus.

The Neutron has no charge but is the same mass as the proton.

Electron

Proton

4 Forces of Nature (Order of strength)

Gravitational

- Only Positive

- Very long range

Weak Nuclear- Associated with beta

decay

Strong Nuclear –

Holds nucleus together

- Very Short Range

Electromagnetic – Positive and negative

Radiation

Decay of nucleus by the emission of a particle or a ray.

Discovered by Henri Becquerel Units 1 Bq is one decay per secondNatural happens without outside

bombardmentArtificial happens due to bombardment

J’ai fais ça !Dodgy

Beard

Safety

Wear Gloves or Apron of lead

Don’t point at anyone

Don’t eat!!!

Nuclear Equations

Top and bottom must add upTop is mass numberBottom is atomic numberProton H Neutron electronAnd Alpha

H11 n10 e10

HeThU 42

23490

23892

Alpha Particles

Helium NucleiPositive ChargeHeavy so not very penetratingVery Ionizing

147N +4

2He 178O + 1

1H

HeThU 42

23490

23892

Beta Particle ß

Fast electron from the nucleus Negative charge Moderately Penetrating Moderately ionizing

147N 14

8O + 0-1 ß

0123491

23490 PaTh

Gamma Ray

High energy e-m wave (A Photon)No charge - not deflected by fieldVery penetrating – Need lead to stop

most of themNot very ionizingRelease energy after reaction

Penetrating Power

Paper Al foil Concrete

 

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Particles in Fields

Charged particles move in a circular path as the force is always at right angles to the direction of motion-

Fleming's Left Hand Rule

RadioactiveSource Cloud

Chamber

Click here for internet demo

Ionisation

We can prove that radiation creates ions as we bring a source close to a charge electroscope

Ionising Power

Alpha is heaviest and so does most damage – poison with Polonium

Beta is only moderately ionisingGamma is only slightly ionising but

difficult to stop

Solid State Detector

P N

This a P-N junction in reverse bias.

This creates a huge depletion layer.

+-

A piece of radiation passes through the depletion layer and creates enough carriers to carry one pulse of current.

Geiger Muller Tube

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Experiments

All experiments the same stick a DETECTOR in front of a source and count the decays.

Move it away for distance and plotTime for half life and plotPut things in front for penetration

Penetration

A Gieger Muller Tube and Counter.

Plot the activity against the thickness or the type of barrier

Distance

A Gieger Muller Tube and Counter.

Plot the activity against the distance r.

r

Half Life

A Gieger Muller Tube and Counter.

Plot the activity against the time

Time it takes for half the atoms to decay

Half-Life – time it takes for half the radioactive particles to decay

Atoms Not Decayed

Time1 2 3 4

Half life demo from internet click here

Half Life Calculations

1000 particles time=6s 2 half-life

500 particles time=9s 3 half-life

250 particles time=12s 4 half-life

125 particles time=15s 5 half-life

4000 particles time=0

2000 particles time=3s 1 half-life

Calculations – we use the decay constant λ in our calculations.

=0.693/T½

=0.693/3s

=0.231s-1

Activity Calculations

Rate of Decay = x number you started with

dN/dt = - x N

Start with 4000 particles and =0.231

Activity = 4000 x 0.231=924 Bq

Calculations

1) You start with 100 grams of sulfur-35, which has a half life of 87.51 days. How much time will it take until only 12.5 grams remain?

How many half lives?100>50>25>12.5 so 3 half livesTime = 3 x 87.51 = 262.53 days

Calculations2) You measure the radioactivity of a substance,

then when measuring it 120 days later, you find that it only has 25 % of the radioactivity it had when you first measured it. What is the half life of that substance?

How many half lives100%>50%>25%2 half lives =120 days1 half life = 60 days

Calculations

3) Your professor gives you 64g of phosphorus-32 (half life = 14.263 days).

(a) What is its decay constant ? (b) What is its activity (Rate of Decay)?

(a) Using the formula =0.693/T½

=0.693/(14.263x24x60x60) = 6.62 x 10-7 s-1

Calculations

3) Your professor gives you 64g of phosphorus-32 (half life = 14.263 days).

(a) What is its decay constant ? (b) What is its activity (Rate of Decay)?

= 6.62 x 10-7 s-1 (b) Using Activity =dN/dt = -N N= Moles x 6x1023 = 2 x 6x1023 Activity = 6.62 x 10-7 x 12x1023 == 7.3 x1017 Bq

Isotopes

Same atomic number different mass number

Isotope pp

Uses of Radioactive Isotopes

Medicine – treatment and imagingSmoke detectors Food IrradiationCarbon-14 Dating

Isotopes

Same Atomic number different Mass number

Carbon-14 Dating

At death all animals contain the same ratio of C-14 to C-12

The rate of decay of C-14 is fixedThe C-14 left tells us how long ago it

died

%C-14

time

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Rutherford Scattering

Do I look like Freddie?

Rutherford on internet

Rutherford Scattering – alpha particles fired at gold foil.

Most pass unaffected - So the nucleus is very small

Rutherford Scattering – alpha particles fired at gold foil.

Nucleus

A small number of high energy alphas are Deflected

Some reflected completely back - Nucleus totally positive.

Rutherford Scattering – alpha particles fired at gold foil.

Nucleus

A small number of high energy alphas are DeflectedMore pass unaffected - So the nucleus is very smallSome reflected completely back - Nucleus totally

positive.

Cockcroft and Walton

Alpha Alpha a

LithiumTarget

Alpha Alpha

Hydrogen discharge tube

Accelerated byAn huge electricField (700000v)

Proton

Alpha strikes the screenProducing a flash thatIs seen with the microscope

Internet explanation

Nobel Prize for Physics

Proton + Lithium 2xAlpha + Energy

Proves Einstein’s Law E=mc2

First Transmutation by artificial Bombardment of an element

Ernest Walton

EnergypLi 42

42

11

73

Binding Energy

The total nucleus weighs less than all its parts

Difference is Mass DefectConverted to energy to hold the nucleus

together

E=mc2

As Iron is the most stable as you go towards it you release energy

So Carbon-12 is lighter than 12 protons The difference is the binding energy

Binding Energy of a Deuteron

A deuteron is the nucleus of a deuterium atom, and consists of one proton and one neutron. The masses of the constituents are:

mproton = 1.007276 u (u is Atomic mass unit) mneutron= 1.008665 u mproton + mneutron = 1.007276 + 1.008665 = 2.015941 u

The mass of the deuteron is: Atomic mass 2H = 2.013553 u

The mass difference = 2.015941 - 2.013553

= 0.002388 u

Convert to Kg

Multiply by conversion factor1u = 1.66x10-27 KgMass = m = (0.002388) x 1.66x10-27

Mass = m = 3.96x10-30 Kg

Use Famous Formula

E=mc2

E= 3.96x10-30 Kg x (3x108 m/s) 2

E = 3.56x10-13 Joules

Fusion – The sun and the stars

Fusion is the joining together of 2 light nuclei to make one nucleus with release of energy.

Caused by a super fast collision at high temperature in a magnetic bottle.

21H 2

1H

Fission

The breaking apart of a heavy nucleus to form smaller nucleus with release of energy.

Caused artificially by the bombardment of the right speed of neutron.

In both fusion and fission the products are lighter than the reactants and the MASS DEFECT is turned into Energy E=mc2

1. Subtract mass in a.m.u.

2. Convert to kg

3. Use E=mc2

Also produced 3 fast neutrons that can cause another fission and so a chain reaction

Uranium-235

Nuclear Equation

EnergynBaKrnU 10

13956

9736

10

23892 3

In the isotope U-238 the neutrons must be slowed down by a moderator - Graphite

Fuel rods contain the Uranium-235 (Enriched to ensure chain reaction)

Moderators (Graphite) slow down the neutrons to the right speed

Control Rods (Boron Steel) absorb neutrons to stop the reaction and prevent meltdown

Heat to heat exchanger prevents Radiation escaping steam to turbine

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Leptons

Fundamental particles

1/1846 of an a.m.u.

Does not feel the strong nuclear force

Matter – Electron , Muon, Tau, ……

Anti-matter – Positron, Anti-Tau

Anti-matter first suggested by Paul Dirac

Annihilation

e+

e-

Matter combining with anti-matter to form energy in the form of e-m radiation

2 photons conserve momentum ?

e+ + e- 2hf (2g)

Annihilation

e+

e-

An electron and a positron collide to make energy.

All the mass of the electrons gets turned into gamma waves

So Energy E=mc2

To find frequency of wave E = 2h.f

Matter turnsInto energy

Matter combining with anti-matter to form energy in the form of e-m radiation

2 photons conserve momentum

Wave made by Anihilation

A proton and a Anti proton. The masses of the constituents are:

mproton = 1.007276 u (u is Atomic mass unit)

mproton + manti = 1.007276 + 1.007276 = 2.014552 u

The mass difference = 2.014552 uTo use this in a calculation we covert to kg

Convert to Kg

Multiply by convertion factor1u = 1.66x10-27

Mass = m = (2.014552) x 1.66x10-27

Mass = m = 3.34x10-27 Kg

Use Famous Formula

E=mc2

E= 3.34x10-27 Kg x (3x108 m/s) 2

E = 3.01x10-10 Joules

Use Planks Equation E=hf

h= planks constant3.01x10-10 Joules = (6.6x10-34 js)x(f)f= 3.01x10-10 Joules / 6.6x10-34 js

= 4.56x1023 Hz

In practice this is low as KE from particles increases this.

Pair Production

e+

e-

An electron and a positron are created from a gamma ray. (We can also get a proton and an anti-proton)

We do the calculation in reverse

To find energy of wave E = h.f

As we get 2 electrons E = 2mc2

A matter and anti-matter pair being created by energy from an e-m wave

Annihilation and Production

p+

p-

New particles are produced from the KE of the colliding protons They must conserve charge

If we carry in 4Gev (1.6x10-19 . 4x109= 6x10-10 J)

As Energy to make 3 Pions is E=mc2 =(3x 2.4842x10-

28xcxc)

=6.7x10-11 J

Subtracting we find the KE after collision.

p+

p-

+

0

-

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Quarks - Inside the Hadrons

6 Quarks6 Anti-Quarks – Opposite Signs

UP

+2/3

STRANGE -1/3

TOP

+2/3

DOWN

-1/3

CHARMED +2/3

BOTTOM -1/3

Hadrons

Baryons Mesons

3 quarks Quark+anti-quark

Proton Pion

uud ud

Feels strong nuclear force

Feels strong nuclear force

Baryon

Meson

Hadrons on internet

Subject to all forces

Particle Zoo

HadronsLeptons

Fundamental particles

Do not feel Strong Nuclear

Force

Baryons

3 Quarks

Protonuud

Mesons

Quark +Anti-quark

Pionud

Ghost Particle Mystery

By 1930 most of the particle physics world was understood

However the decay of the neutron to a proton producing a beta particle did not obey Einstein's Law

n0 → p+ + e-

Pauli said there must be a new particle called a neutrino

Beta decay

In β− decay, the weak force converts a neutron into a proton while emitting an electron and an antineutrino

n0 → p+ + e- + νe

This explains loss in energy and momentum. Pauli

proposed it’s existence in 1930 but was not

discovered until 1956 as it is so weakly interacting

with other particles.

Nuclear Formula

00

01

11

10 pn

Particle Accelerators-Linear

Very high Voltage electric fields

Electro-magnetic attraction pulls particles down.

Circular Accelerators

Particles spiral in fields (Flemings Left hand rule)

Cyclotron- We put the field at right angles e more power with oscillating field

CERN

Particles can travel in opposite directions and double the collision energy

Magnets force particles in

circular path so stay in tube

Circular more

compact

High velocity needed to overcome repulsion

Vacuum to avoid collisions increase mean

free path

More velocity more KE so more new

particles made

Detectors

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H/W Roundup (Yeh har)

2007 q112004 q102003 q112005 q12(d)2006 q 92003 10(a)