Particle Physics Tutorial 5 - Fundamental Forces


What holds the nucleus together?

There are four fundamental forces that are responsible for all phenomena (things that happen) in physics, and all the forces that we can name can be explained in terms of these fundamental forces.  They are gravity, electromagnetic force, strong nuclear force, and the weak nuclear force.



Gravity is always attractive.  It is never repulsive.  It is a property of bodies with mass, but is very weak indeed.  The only reason we feel gravity at all is that the Earth is a huge object, of mass 6 ◊ 1024  kg.  Gravity is responsible for the Universe the way we see it today.


At the nuclear level, gravity is far too small to be responsible for nuclear phenomena.  It is thought to be mediated by a particle called the graviton, but such a particle has never been observed.  Since the range is infinite, and stars and planets are attracting each other all the time, presumably the Universe must be crawling with the little brutes.



Electromagnetic Force

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.

This graph tells us that if we pull two atoms apart, there is an attractive force from the bonds that pulls the atoms back together.  If we squash the two atoms together, there is a large repulsive force that pushes them apart.  At a distance that is about the radius of an atom, the two atoms will experience zero force.


The electromagnetic force is transferred or mediated by the virtual photon.  This means you can't see it in action (in other words, you don't get flashes of light from your bottom when you sit down).  If you see the photon, it means it's not being involved in the electromagnetic force.  Virtual particles have only a very short lifetime.


Question 1

Two protons experience a repulsive force of about 200 N when they are packed together in a helium nucleus.

(a)  Explain why this is the case.                                                                                 

(b) Use a = F/m to work out the acceleration of the protons if they were released.    

(c) What stops them from flying apart?                                                                         




The Strong Nuclear Force

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 200 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, in the order of 10-15 m, or 1 femtometre.



We can draw a very similar graph to the one above to show what happens when we pull two nucleons apart, or squash them together.


The strong force is mediated by gluons which bind the nucleons together.  All hadrons feel the strong force.


The Weak Nuclear Force

There is another force that is only found within the nucleus, the weak nuclear force, which is responsible for beta minus decay.  The weak force has a very short range, about 10-18 m.  In beta decay, things happen that cannot be explained by the action of the electromagnetic force, gravity, or the strong force.  There is a theory that itís actually another form of the electromagnetic force.  The weak force is poorly understood. 


The weak force is mediated by the W and Z bosons:

Question 2

What forces are responsible for:   

Chemical reactions


Attraction between two planets.


Beta decay


Holding the nucleus together




Comparing the forces

We can sum the forces up in this diagram:



The table shows the strength of the forces relative to gravity:



Acts on

Range (m)

Relative strength

Mediated by


All objects with mass





Charged objects





Quarks and nucleons

1 ◊ 10-15





1 ◊ 10-18


W+, W-, and Z Bosons



Question 3

 Look at the graph to the below:

(a)  What does a positive value of force indicate?                            

(b)  What is happening at point A?                               

(c) What is happening at Point B?                                                        

(d) Which point indicates that a pulling force is being applied?                

(e)  At which point do the two atoms come apart?  Explain your answer. 

(f)  Which fundamental force is responsible for what we see in this situation?         




Exchange Particles

All forces are mediated by exchange particles which carry momentum and energy from one particle to the other.  The simplest model to understand their action is like this:

Each particle in this model is represented by a boy on a skateboard.  Particle A throws a ball to Particle B who catches it.  Since momentum has to be conserved, Particle A moves to the left as he throws the ball.  Particle B moves to the right as he catches the ball.  So the two boys move apart.

This models a repulsive force.


If we want to model an attractive force, we use the idea of a boomerang.

Particle B throws the boomerang towards his mate, Particle A.  As he throws it, conservation of momentum dictates that he must move to the left.  Particle A catches it and the boomerang transfers momentum, moving Particle A to the right.  The two boys move together.


This may sound strange, but:

Mass and energy are interchangeable at the sub-nuclear level.


Question 4

The diagrams above show how forces behave at the atomic level. Use the model to explain how the electromagnetic force acts between two charge particles that are:

a. Like-charged;

b. Oppositely charged.




All exchange particles are bosons.  Not all bosons are exchange particles.  Mesons are bosons but are not exchange particles.  We will look at mesons in a later tutorial.  Exchange particles are sometimes called gauge bosons.  There is more about this in Tutorial 12.


There is another family of particles called fermions.  The fermions include leptons, quarks, and baryons.  The division is the result of a mathematical theory, not through direct observation.  However observations have supported what the theory has predicted.


Particles have the quantum numbers of spin.  Some particle models have the idea that the particles are tiny spinning objects.   Bosons have a whole number value of spin.  Fermions have half values of spin, for example, 1/2, 3/2, and 5/2.  This is beyond what you need to know.


Bosons are allowed by quantum theory to do the same thing together.  Photons are allowed to do exactly the same thing, which is why a laser can make photons march precisely in step.  This results in a very narrow beam of intense light.  Fermions are not allowed to do the same thing at the same time.  Therefore two electrons are not allowed to be in the same orbit at the same time (the Pauli Exclusion Principle).  Therefore you can't make a laser from electrons.


The gauge boson properties are shown in the table:




Rest Energy







Virtual Photon





0.002 eV

3 ◊ 10-15 m


W+, W-, Z0

W = 80 GeV

Z = 90 GeV

1 ◊ 10-18 m




Grand Unification Theories

Physicists have always liked patterns.  James Clerk-Maxwell showed that electrical forces and magnetic forces were different versions of the same thing.  The question that is exercising physicists at the moment is whether all four fundamental forces are different versions of the same thing.  There has been evidence produced to suggest that the electromagnetic and the weak forces are different versions of the same thing, the so-called "electro-weak theory".


The driving force behind machines such as the large hadron collider is to reproduce the extreme conditions immediately after the Big Bang, the titanic explosion that is thought to be the start of the Universe.  The theoretical physicist, Peter Higgs, proposed some years ago that there was a particle, the Higgs boson, that mediated all the fundamental forces.  This would prove that all the forces were really one and the same thing, the grand unification theory


Evidence for its existence was discovered at CERN in 2013.  It is thought to be a massive particle of rest energy 126 GeV.  It required many high energy collisions and interpretation of particle tracks by supercomputers to show evidence of its existence.  CERN have published this image:


Image by CERN