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Sunday, November 28, 2021

# Topic 5.  Probing the Nucleus

The Story so far…

In the early days, the atom was thought to be fundamental.  It was considered to be a blob of protons with electrons mixed in.

Then the physicist Ernest Rutherford came up with a Mark 2 version, a positive nucleus surrounded by a cloud of negative electrons.

Version 3.0 came about with the discovery of the neutron in 1921, giving us the Bohr model of the atom.  (Niels Bohr was goalkeeper for the Danish Olympic Football team in 1908.)

This is the model that you would have used in Chemistry and Physics.

The arrangement of electrons was worked out by Erwin Schrödinger during a dirty weekend! Nowadays physicists have worked out a version 4 of the atom, which is called the Standard Model.  The electrons are as before, but the protons and neutrons are made up of quarks.

Observing Smaller and Smaller Objects

Whenever we observe something, we need three different pieces of apparatus:

• illumination (some kind of radiation)
• the object under study
• detector

If you read a book, your eyes detect the changes caused by the effect of ink on paper (the object) in response to light (radiation).

However the light is limited by its wavelength to resolving objects about 1 mm across.  Much less than that, then diffraction becomes important.  Waves will not travel through a gap less than a wavelength.  Light wavelengths cannot resolve atoms.  Shorter wavelengths can be used but the eye cannot detect these.

X-rays can be used to resolve individual atoms by X-ray crystallography.

The wave properties of electrons can be harnessed in electron microscopy.  We can resolve the structure of individual molecules, but not the structure of the atoms themselves.

The key point to bear in mind at the microscopic level is that:

• Waves can be thought of as particles
•  Particles have wave properties
• Energy and mass are interchangeable, linked by Einstein’s equation E = mc2.

To resolve the structure of atoms we need a very powerful microscope, several metres long.  This gives us very high-energy particles with a very short de Broglie wavelength.  The two pictures show a light microscope and an electron microscope.

Energies of particles are expressed in electron-volts (eV) where:

1 eV = 1.6 x 10-19

To see various levels of detail requires the following kinds of particle energies

• 100 eV                         –  the electron cloud around the nucleus
•  100 MeV (1 x 108eV)  –  the nucleus itself
• 10 GeV (1 x 1010eV)    –  the fine structure of the nucleus.

Therefore to resolve parts of the nucleus needs very high particle energies to gain short de Broglie wavelengths.  However, there’s a problem.  At these energies the particles have an unfortunate habit in smashing up the nuclei; a bit like asking a bull for a commentary on fine antique porcelain.

Question 1 What is the energy in joules of the following electron energies?  ANSWER

From these energies in joules, we can work out the speeds at which the electrons travel using v= 2 Ek/m.  Mass of an electron = 9.11 × 10-31 kg.

Question 2  What is the speed of an electron at an energy of 100 eV and at 10 GeV?  ANSWER

The last answer gives us a speed of an electron that is faster than the speed of light.  In fact we cannot go faster than the speed of light.  A different (and more complex) equation is needed as the speed of the electron gets towards the speed of light.

We can also get short de Broglie wavelengths using heavier particles like alpha particles.

What holds the nucleus together?

There are four fundamental forces that are responsible for all phenomena in physics, and all the forces that we can name can be explained in terms of these fundamental forces.  They are gravityelectromagnetic forcestrong nuclear force, and the weak nuclear force.

Gravity is a weak force, but it holds galaxies together.  At the nuclear level, gravity is too small to be responsible for nuclear phenomena.

Electromagnetic forces are observed in the interactions between atoms.  We know how atoms have a positively charged nucleus surrounded by a cloud of negatively charged electrons.  Molecules are bound together by electrical forces, which have an infinite range, and can be attractive or repulsive. The mechanisms for chemical reactions can be explained in terms of the electromagnetic force at the atomic level.

However, we know that the positively charged nucleus is very tiny, about one ten thousandth the size of an atom.  We also know that positives repel.  We can do a calculation on two positive charges to find that a force of about 2 N exists between them.  So why does the nucleus not fly apart?  There is a force that stops this, the strong nuclear force.  It is very short range.

The weak nuclear force is very short range, about 10-15 m.  It is responsible for beta minus (and beta plus) decay.  It is thought to be a version of the electromagnetic force.

 Question 3  What forces are responsible for: Chemical reactions Attraction between big objects Beta decay Holding the nucleus together

Fundamental Particles

Particle physics is concerned with fundamental particles, which means that the particles can’t be broken down any further..  It used to be thought that protons, neutrons and electrons were the fundamental particles of matter.  However it has been found that nucleons (proton and neutron) are made up of smaller particles, so nucleons are now not fundamental.

Particles and antiparticles

Each particle has an antiparticle.  However, antiparticles are not found in normal matter, but arise in:

• high-energy collision experiments,
• interactions with cosmic rays,

We should note the following:

• an antiparticle has the same mass as its particle,
• a particle and its antiparticle have equal but opposite charge
• an unstable particle and its antiparticle have the same lifetime.
• some neutral particles and their antiparticles are identical (e.g. photon and po meson)
• other neutral particles and antiparticles are not identical.

Antiparticles can be made in large quantities in accelerators, resulting from high-energy collisions.  They have short lifetimes, about 10-10 s because when they meet their equivalent particle, they annihilate each other in a burst of energy.   It is even possible to make simple antiatoms.

It is thought that there is more matter than antimatter in the Universe.   It is not impossible that antimatter exists in large quantities somewhere, and that there are antimatter stars and planets.  None have yet been detected.

 Question 4 Complete this table.  Some have been done as an example: Particle Mass compared with proton Charge Electron 1/1800 -1e Positron Proton Antiproton Neutron Antineutron

Families of Particles

Let us look at the families of particles:

•  Leptons – fundamental particles such as the electron.  They are called leptons as they are considered to be light-weights, although some of them are as massive as mesons.
•  Hadrons – these are made up of quarks (pronounced ‘quork’ as in pork).  There are two families:
1.  The mesons which consist of one quark and one antiquark.
2.  The baryons, which consist of three quarks.
 Question 5  Complete the table. Particle type Structure Leptons Meson Hadron

Leptons

There are six particle-antiparticle pairs known.  Leptons (Greek – “light thing” or “small coins”) are the smallest of the fundamental particles.  They have the following properties:

• fundamental particles without structure
• they interact by the weak interaction.  If they are charged, they interact by the electromagnetic interaction, but NOT the strong interaction.
• charge and lepton number are conserved in all allowed lepton processes.

There are three categories of lepton number, Le, Lm, and Lt.  Each lepton has a lepton number, 0 or 1, in each category, and each antilepton has a number 0 or -1 in each category.  You need to know the lepton numbers.

The names of the leptons are:

Lepton

# Charge

Lepton Number
electron e- -1e L= 1, Lm, & Lt = 0
electron neutrino ne 0 L= 1, Lm, & Lt = 0
muon m- -1e L= 1, Le, & Lt = 0
neutrino nm 0 L= 1, Le, & Lt = 0
tau t- -1e L= 1, Lm, & Le = 0
tau neutrino nt 0 L= 1, Lm, & Le = 0

Each particle has an antiparticle; for the electron, it is the positron, the muon the antimuon, and the tau, the antitau.  We show the anti-particle either by an opposite charge (e+) or by putting a bar across the symbol.

Question 6.  What is the symbol, the charge, and the lepton number of the particle antitau?  ANSWER

Consider this decay:

Notice how the lepton number and charge are conserved.  This means that the decay can proceed.  If leptons interact with hadrons, the hadrons are considered to have a lepton number of 0.

Question 7 Will this reaction work?

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