Probing Deep into Matter

Question 1

Describe Rutherford’s experiment.

Answer 1

A stream of alpha particles (⁴₂He²⁺) was fired at a thin piece of gold foil.

The number of alpha particles scattered by the foil was recorded.

It was noted that some particles scattered at angles greater than 90° to the foil.

This suggested that the alpha particles were colliding with something more massive than themselves.

Question 2

What were the conclusions of Rutherford’s experiment?

Answer 2

The atom is mostly empty space - the majority of alpha particles went straight through the foil.

The centre of the atom must be tiny but massive - some α particles were deflected at large angles.

The α particles were repelled, suggesting that the nucleus is positively charged.

Atoms are neutral overall, therefore the electrons must be on the outside and the nucleus in the centre.

Question 3

What is the closest approach of a positively charged particle to a nucleus?

Answer 3

The point where the particle’s electrical potential energy is equal to its initial kinetic energy.

1/2mv² = Qq/4πε₀r

Where: Q = charge on the nucleus (proton no. x proton charge)

q = charge on the particle

ε₀ = permittivity of free space

r = closest approach

Question 4

What are the units of permittivity?

Answer 4

F/m

Farads per metre

Question 5

Define a hadron. What particles classes are hadrons? What particles are hadrons?

Answer 5

A particle that feels the strong force. Baryons and mesons. Protons and neutrons are hadrons.

Question 6

What is a baryon?

Answer 6

A nucleon - a proton or neutron (or a sigma baryon).

Question 7

What becomes of all baryons?

Answer 7

They all decay into protons.

Question 8

Define a lepton.

Answer 8

A lepton is a fundamental particle which does not feel the strong force. They are only able to interact via. gravity and the weak force.

Question 9

Give four examples of leptons.

Answer 9

Electrons, muons, taus and neutrinos.

Question 10

What are muons and taus? What are they counted as in nuclear reactions?

Answer 10

More massive electrons. A muon is counted under L_μ and a tau is counted under L_τ. Additionally, an electron is counted under L_e.

Question 11

What is a neutrino? What is its symbol?

Answer 11

Each lepton has a neutrino - a chargless, almost massless particle which rarely reacts with normal matter.

ν_e , ν_μ, ν_τ

Question 12

What are neutrinos counted as when balancing particle reactions?

Answer 12

Their respective leptons - i.e. a tau neutrino would be counted under L_τ.

Question 13

What becomes of muons and taus?

Answer 13

They decay into electrons.

Question 14

What is the lepton number of an anti-neutrino, ( ̅ν)?

Answer 14

-1

Question 15

What is the equation for neutron decay?

Answer 15

n —> p + e^- + ̅ν_e

n = neutron (+B)

p = proton (+B)

e^- = electron (+L_e)

̅ν_e = electron anti-neutrino (-L_e)

Question 16

What is an antiparticle?

Answer 16

A particle which has the opposite charge and equivalent mass to its counterpart (i.e. electron and positron), and has a -1 lepton or baryon number, depending on the particle it opposes.

Question 17

What does E=mc² mean?

Answer 17

That mass and energy are equivalent and therefore interchangable.

Question 18

How much antimatter and matter are made when matter is converted to mass?

Answer 18

Equal amounts - pair-production is the creation of the same amount of matter and antimatter when energy is converted to matter.

Question 19

What is pair production and when does it occur?

Answer 19

Pair-production is the conversion of energy into matter. It occurs when a gamma ray photon (γ) passes close to a nucleus and has enough energy to form however much .

Question 20

Why does pair production only occur close to a nucleus?

Answer 20

To allow momentum to be conserved within the system.

Question 21

What is the diagram for pair production?

Answer 21

A gamma ray photon forming an electron and positron.

Question 22

What happens when a particle and its antiparticle meet?

Answer 22

They annihilate, producing energy in the form of a gamma ray photon.

Question 23

What are the constituents of a hadron?

Answer 23

Quarks

Question 24

What is antimatter made up of?

Answer 24

Antiquarks

Question 25

What are the types of quark?

Answer 25

Up, down, charm, strange, bottom, top.

Question 26

What are the baryons numbers of up, down and strange quarks?

Answer 26

Up - +1/3

Down - +1/3

Strange - +1/3

Question 27

What is the strangeness of up, down and strange quarks?

Answer 27

Up - 0

Down - 0

Strange - -1

Question 28

What are the charges on an up, down and strange quark?

Answer 28

Up - +2/3

Down - -1/3

Strange - -1/3

Question 29

What is the baryon, charge and strangeness of antiquarks?

Answer 29

Anti-Up - B = -1/3, C = -2/3, S = 0

Anti-Down - B = -1/3, C = +1/3, S = 0

Anti-Strange - B = -1/3, C = +1/3, S =+1

Question 30

What are baryons made up of?

Answer 30

3 quarks.

Question 31

What is the evidence for baryons being made up of three quarks?

Answer 31

Firing high-energy electrons at a proton is the evidence - the electrons scattered in such a way as to suggest that their are three concentrations of charge in a proton.

Question 32

What are the constituent quarks of a proton?

Answer 32

uud

Question 33

What are the constituents of a neutron?

Answer 33

udd

Question 34

How are particles able to interact?

Answer 34

By exchanging a particle, called a gauge boson, which carries the necessary momentum for attraction or repulsion.

Question 35

What particles are affected by the strong force, and what is the gauge boson for this interaction?

Answer 35

Hadrons are the only particles affected by the strong force. The gauge boson for the interaction is the gluon.

Question 36

What is the gauge boson for electromagnetic interactions? What particles does this boson affect?

Answer 36

The photon is the gauge boson for electromagnetic interaction. The photon can only be exchanged by charged particles.

Question 37

What particles does the weak force exert itself over? What is the gauge boson for the weak force?

Answer 37

The weak force affects all particles, and has three gauge bosons - W⁺, W^-, Z^o.

Question 38

What is the gauge boson for gravitational interactions? What particles can exchange this boson?

Answer 38

The graviton is the gauge boson for gravitational interactions and it can be exchanged by all particles.

Question 39

Why is it that trying to seperate quarks results in the production of a quark and antiquark?

Answer 39

Trying to seperate quarks increases the energy of their gluon field, increasing the attractive force between the quarks. This field continues to build in energy as the quark is further seperated from its counterparts until, once the energy of the field is large enough, the energy is converted to mass in the form of an quark-antiquark pair.

Question 40

Describe a linear particle accelerator.

Answer 40

A long straight tube containing a series of electrodes - an alternating current is supplied to the electrodes such that their charge changes so that the particles are attracted to the next electrode and repelled from the previous one

Question 41

Describe a cyclotron.

Answer 41

A circular particle accelerator, split into two halves - an alternating p.d. is supplied to each side in opposition, accelerating the particles between each half. A magnetic field runs perpendicular to the dish face, causing the charged particles to move in a circle - the electric and magnetic fields cause the particles to spiral outwards as their kinetic energy increases.

Question 42

What is a synchotron?

Answer 42

A cyclotron in which the strength of the magnetic field is increased to keep a beam of high-energy particles moving in a circle, and the electrodes are positioned along the length of the circle to accelerate the beam.

Question 43

Why is not possible for mass to reach the speed of light?

Answer 43

Special relativity - as a mass travels at a higher velocity, its kinetic energy increases. Because of mass-energy equivalence, the mass becomes more massive, requiring more energy to accelerate it further.

Question 44

What is the relativistic factor equal to?

Answer 44

γ = E_total / E_rest

γ = 1 / ( 1 - ( v² / c² ) )

Question 45

Is potential energy defined as a positive quantity or a negative quantity?

Answer 45

Negative - it is able to do work on its surroundings

Question 46

Why is it that atoms are only able to emit certain wavelengths of light?

Answer 46

When electrons move down energy levels, they emit photons of an energy equal to the difference between the energy levels. Because energy levels have definite values, only certain energies (And thus wavelengths) of photon can be emitted.

Question 47

What is the defining feature of a fermion? Give three examples of fermions.

Answer 47

They adhere to the Pauli exclusion principle - no two fermions can occupy the same quantum state at the same time.

Protons, neutrons and electrons are all fermions.

Question 48

What evidence is there that energy levels are of a definite potential energy value?

Answer 48

Absorption and emission spectra - cool gases absorb certain frequencies of light when their atoms’ electrons are excited from their ground state; hot gases emit particular wavelengths of light when their atoms’ electrons descend energy levels and emit a photon.

Question 49

What is the wave model of an atom?

Answer 49

The model which treats electrons in orbit around a nucleus as a standing wave.

Question 50

What is the De Broglie relationship?

Answer 50

λ = h/mv

Where:

λ = wavelength

m = mass of the object

v = velocity of the object

Question 51

Why is it that electrons can only have certain wavelengths?

Answer 51

Because there wavelength must equate to an 1/n times the circumference of the electrons’ orbit, where n is an integer - the electrons exist as standing waves.

Question 52

What is the principal quantum number of an electron?

Answer 52

The number of complete waves of that electron which fit around the circumference of its orbit.

Question 53

What is the energy of an energy level equal to?

Answer 53

-13.6eV / n²

Where n is the number of complete waves that fit the circumference of the electrons’ orbit.

Question 54

Why is it that as the number of complete electron wavelengths that fit that electron’s orbit increases, the potential energy of the electrons decreases?

Answer 54

Because the electron is further from the nucleus, its potential energy is lower. Because the electron is further from the nucleus, the circumference of its orbit is greater, meaning that number of complete wavelengths which fit it is greater.