Physics 452.3 & 851.3Physics 452.3 & 851.3 Subatomic PhysicsSubatomic Physics

Web site:physics.usask.ca/~pywell/p452

Subatomic PhysicsSubatomic PhysicsThis course is an introduction to Nuclear Physics and

Particle PhysicsSubatomic physics is really about getting to the heart

of what we know about the Universe.i.e. We are trying to answer the fundamental

questions What is the Universe made of?

the particles What are the interactions between them?

the forces What are the overarching rules that govern all

things in the Universe? the conservation laws or symmetries

Rutherford ScatteringRutherford ScatteringThe experiment carried out by Geiger and

Marsden.First established that the atom is composed of

a small nucleus surrounded by electrons.The experiment made use of -particles.

RadioactivityRadioactivityIf we put some radioactive material in front of a

magnet we see 3 types of radiation.

radioactive materiale.g. Uranium magnetic field

-rays

-rays

-rays

- particles charge +2e mass ~ 7000me= nucleus of helium atoms

-

particles

charge 1e mass = me= electrons

- rays

no charge

no mass= photons (high energy X-rays)

Geiger and Marsden ExperimentGeiger and Marsden Experiment

They counted the number of -particles scattered in each direction .

They found that most of them pass through without deflection.

But one in several thousand are scattered by angles > 90

-particles

scintillating screen

microscope

gold foil

RutherfordRutherfords Explanations Explanation Atom is mostly empty. Atom has a small positively charged nucleus

containing most of the mass of the atom. It was postulated that the electrons were in

orbit about the nucleus. Number of electrons = Z = Atomic Number

determines atoms position in the periodic table (chemical properties)

Therefore Nucleus has charge +Ze

(so that atom is electrically neutral)

RutherfordRutherfords Explanations ExplanationUsing this model, Rutherford was able to derive the

shape of the Angular Distribution of the scattered -particles that was observed by Geiger and Marsden.

To do this he assumed: The target nucleus has negligible recoil

i.e. it is much more massive than the -particle The only force between the -particle and the

nucleus is the Coulomb force. i.e.

nucleus and between distance where

))(2(4

1)(0

r

rZeerV

RutherfordRutherfords Explanations ExplanationHe also assumed: Classical mechanics can be used. Elastic Scattering

i.e. the collision between the -particle and the nucleus is an elastic collision.

(There are no excitations of the nucleus or the -particle we are getting ahead of ourselves here!)

For now, we will not go through the derivation of the Rutherford scattering formula.

The result is:The Probability of scattering at angle is

particle-incident of KE where

2sin1)( 42

2

T

TZP

Rutherford ScatteringRutherford Scattering

We see that this formula predicts A large probability for small A small probability for large

Is this a problem? 0 corresponds to a large Impact Parameter b

particle-incident of KE where

2sin1)( 42

2

T

TZP

)(0 P

b

Rutherford ScatteringRutherford Scattering Geiger and Marsden

showed that the Rutherford formula was correct. Agreed for angles

P() was proportional to Z2 1505

2sin1)( 42

2

TZP

Rutherford ScatteringRutherford ScatteringLater, Rutherford and Chadwick showed that there was no

deviation from the formula for a large range of -particle energies.

i.e. There is no deviation from Coulombs Law.This means that there is no collision between the -particle

and the nucleus.(At least for the -particle energies available to them at the time.)

This means that both the -particle and the nucleus had to be very small!

Eventually deviations from the Rutherford formula were found when the closest approach of an -particle to the nucleus was ~ 8

1015 m.

This was the first estimate of the nuclear size.

The NucleusThe NucleusA remaining puzzle was the existence of isotopes.Isotopes = Atoms with the same Z (chemical

properties) but different masses.This was explained by Rutherfords postulate that the

nucleus consisted of two types of particles.Protons: = Nucleus of neutral Hydrogen: charge +eNeutrons: No charge but mass ~ mass of proton.This postulate was confirmed by Chadwicks

discovery of the neutron. (via a nuclear reaction)

Nomenclature and DefinitionsNomenclature and DefinitionsZ = # protons = Atomic NumberN = # neutrons = Neutron NumberA = N + Z = Atomic Mass Number

= # Nucleons (protons or neutrons)

Nuclide = name for a specific nucleus

Notation: e.g. NAZ Symbol Chemical

7136 C

Nomenclature and DefinitionsNomenclature and DefinitionsIsotope = nuclides with same Ze.g. Isotopes of Hydrogen

Isotone = nuclides with same Ne.g.

Isobar = nuclides with same Ae.g.

2311

210

11 H H H

Deuterium (d) Tritium

2422

31 He H

71478

146 N C

Nomenclature and DefinitionsNomenclature and DefinitionsAtomic Weight or Atomic Mass

= the mass of an atom (it includes the mass of the electrons)

It is convenient to use Atomic Mass Units (u)(Old abbreviation a.m.u.)

Defined by:

e.g. Atomic mass of = 12.000 uAtomic mass of carbon = 12.011 u

(Average of mass of carbon atoms with the terrestrial abundances of the isotopes of carbon.)

227126 MeV/c 931.5kg 10661.1

12atom Cof Massu 1

C126

Nomenclature and DefinitionsNomenclature and DefinitionsIn these units:Mass of proton:

mp = 1.007276 u = 938.27 MeV/c2.Mass of neutron:

mn = 1.008665 u = 939.57 MeV/c2.Mass of 1H atom:

mH = 1.007825 u = 938.79 MeV/c2.

Nuclear SizeNuclear SizeLater we will see that Nuclear radii are given

approximately by with a = const.

1.2 fm

1 fm = 1 femtometre = 1015 m = 1 fermiThis implies that Volume of nucleus is

proportional to A.This suggests that nucleons have a fixed size.

31aAR

Nuclear Binding EnergyNuclear Binding EnergyThe nucleons in a nucleus remain together

because they are in a lower energy state than if they were apart.

Binding Energy, B= energy needed to make

Nomenclature:M(Z, A) = mass of nucleus.MA (Z, A) = Atomic mass of (includes the

mass of the electrons)

protons free neutrons free ZNX NAZ

NAZ X

NAZ X

Physics 452.3 & 851.3Subatomic PhysicsSubatomic PhysicsRutherford ScatteringRadioactivityGeiger and Marsden ExperimentRutherfords ExplanationRutherfords ExplanationRutherfords ExplanationRutherford ScatteringRutherford ScatteringRutherford ScatteringThe NucleusNomenclature and DefinitionsNomenclature and DefinitionsNomenclature and DefinitionsNomenclature and DefinitionsNuclear SizeNuclear Binding Energy