Radioactive Physics - Alpha, Beta & Gamma Radiation

Nucleur model of an atom

Scientist used to believe that the atom was a neutral charged object which had negative charges evenly spaced

This was known as the plum pudding model

However, Scientists realised that the atom follows a different model and this was proven by Rutherford's alpha scattering experiment

Alpha particles where ejected towards a thin gold leaf and there were different observations

The observations of this experiment must be remembered.

• Most of the particles passed straight through the gold leaf

This is because, the atom is mostly empty space and this also shows that the positive & negative charges are not evenly spaced.

• Few were deflected by a slight angle of less than 90°

This is because when the alpha particles passes near the nucleus they are deflected by a bit. This shows the nucleus is positively charged and so the alpha particles +2 experiences a repulsive force

• Very few only deflected completely or by an angle over 90°

This is around 1/20000 alpha particles and this shows that the nucleus of an atom is so tiny and densed at the center and positively charged. When alpha particle collide head on or sideways to the nucleus, they will deflect by an angle more that 90°

Deflection diagrams

You will need to know how to draw some of these deflections



1. Most pass through without any deflection

2. Some pass with little deflection

3. Very few pass with a large deflections especially when the alpha particle collides with the tiny positive nucleus

Also compare the idea of the plum pudding model and Rutherford's experiment.

Basic Definitions

You will need to know some basic terms of an atom

Let us first see the structure of an atom




Nucleus

It contains both neutrons and protons of the atom and so it's positively charged. Why? This is because, neutrons are neutral and protons are positively charged. The nucleus is very small and highly densed and is at the center of the atom.




Electrons

These are known to be fundamental particles which orbit around the nucleus of an atom in energy levels. If you need to know more go to the leptons section.

The Key




Atomic Number ( Z )

The total number of protons in the nucleus of an atom

The proton number of an atom identifies the element. This is a fundamental fact and this proves that isotopes are of the same element




Mass Number ( A )

The total number of protons and neutrons in the nucleus of an atom

It is the same as the nucleon number

Particles in the nucleus of an atom are called nucleons. So if there are 7 protons and 8 neutrons, it has 15 nucleons.




Isotopes

Atoms of the same element with the same number of protons but, different number of neutrons

The definition defines only atoms and not for ions

So really we usually compare atoms rather than ions so that's why isotopes usually have the same chemical properties because, they have the same number of electrons in the valence shell

However, the physical properties will be different such as the melting point and the density

This is because, the Physical properties depends on the nucleur properties of an atom and the number of electrons determine the chemical properties




So isotopes are always neutral and have the same proton number but, have different neutron or mass number




Nucleur density

It is the mass of the nucleus per unit volume of the nucleus of the atom

Nucleur density = Mass/Volume

To calculate the mass of the nucleus, we must find the total number of neutrons and protons (nucleon number). We also need to remember that the mass of a proton is same as the mass of a neutron and it is 1.67*10^-27kg

So we Multiply to find the total mass

Mass of nucleus = Nucleon number * 1.67*10^-27kg

To find the volume of the nucleus, we need to to know the diameter of a typical nucleus is 10^-15m. Most of the time they will give it.

Volume = 4/3 * πr³

Nucleur density = Mass/volume

You will notice something. That the density is extremely high. This is because, the nucleus is strongly packed using strong nucleur force. But why is the real density way less than the nucleur density?

This is also because, the atom is mostly empty space and so combining the density of the empty space and the tiny densed nucleus will give an overall density which is alot less




Radioactive decay

It is the spontaneous random decay of a unstable nucleus by emiting ionising radiation inorder to be stable

These release radiations such as alpha beta and gamma radiation.

We will need to know some terms



• Random

The time taken for a particle to decay is unknown or random. However, as an overall picture, the average time can be found by using the Decay constant



• Spontaneous

The rate of the decay is not affected by external factors such as temperature



• Ionisation

The ability to strip electrons from a gas molecule to form gaseous ions

Remember that a particle can ionise another atom if it has sufficient energy or charge

• Penetration

The ability for a radiation to pass through materials




Laws conserved during decay

So what laws are conserved during decay:

• Law of conservation of charge and nucleon number
• Law of conservation of Mass-energy

So at both sides the mass-energy is conserved. The products usually have less mass than the reactants but, the fast moving Beta particle(or any radiation) is created. The energy due to this kinetic energy compensates this loss in mass. This is called the mass-energy conservation.

• Law of conservation of momentum

Usually we don't see this in normal equations but, momentum is always conserved.

Types of radiation

There are 3 types of radiation we must know and their characteristics

Type	Nucleur symbol	Nature of radiation
Alpha radiation	He - 4 or 42α	It's a helium nucleus with 2 protons and 2 neutrons
Beta radiation	- e or 0-1β	It is a fast moving electron
Gamma radiation	γ	It is a high frequency electromagnetic wave or a gamma photon

Now we will check their ionisation and penetration

Type	Ionisation	Penetration
Alpha radiation	Greatest ionisation	Lowest penetration
Beta radiation	Medium ionisation	Medium penetration
Gamma radiation	Least Ionisation	Highest penetration

Alpha has the lowest penetration and greatest ionisation as it has the highest charge of 2+ and it is also the slowest. So it has a greater ionisation effect and because it ionises more it loses more energy and thus can't penetrate far. Also alpha particles are stopped by a few cm of air or a sheet of paper or skin

Beta has medium penetration and ionisation as it is charged but, way faster. So it has greater penetration. It is stopped by few cm of aluminum

Gamma has the least ionisation and due to this, it has the greatest penetration. It is never truly stopped but, reduced almost completely by some cm of lead or few meters of concrete




We will see some more details

Type	Speed in terms of c	KE
Alpha radiation	5%c	More than β
Beta radiation	99%c	Range of KE as due to range of speeds
Gamma radiation	c	High - depends on the frequency- usually a specific value. Whereas, beta always changes.




Alpha decay



Always remember that during alpha decay, the nucleon number decreases by 4 and the proton number decreases by 2.

And a helium - 4 nucleus is formed




Beta decay

Remember that there are 2 types of beta decay so we will evaluate each:

• Beta(-) decay

This is usually the default decay whenever they talk about beta decay



Always in beta(-), an neutron becomes an electron and a proton and so The Nucleon number or mass number never changes but only the proton number increases by 1 and so it becomes the next element. Also an electron antineutrino is formed.



We need to know that a down quark is turned into an up quark due to the weak force during this process

Neutron → Proton

ddu → uud

d → u

Why? was an electron antineutrino formed rather than a neutrino?

• Beta(+) decay

In this a proton is converted to a neutron and a positron and a electron neutrino



Always the Mass number remains constant in any beta decay but in beta (+) the atomic number decreases to form the stable product.

Also you need to know that an up quark turns into a down quark during this process

Proton → Neutron

uud → ddu

u → d




Gamma radiation

There is no change in Mass number or proton number as no particles are released except energy. So this allows particles to release excess energy.




Magnetic fields and electric fields

As gamma radiation is neutral, it is not deflected by an electric field or a magnetic field

Beta and alpha are deflected in an electric field



Always as alpha is +2 it deflects towards the negative plate, whereas the beta particle deflects towards the positive plate. However, as beta particle has a lower mass to charge ratio, the deflection is relatively higher than alpha particle.

So when we usually compare the deflection of the same charge to find which one has the greater deflection we use this equation

Deflection ∝ 1/(mass/charge)

For example, a proton has a mass of 1 and a charge of +1

It has a mass to charge ratio of 1.

Another particle of charge +2 and a mass of 4 has a mass to charge ratio of 2

So relative to the first one the alpha particle has twice the mass-charge and so twice as less deflection or further apart




Alpha and beta rays are both deflected in a magnetic field but, gamma rays are not deflected.



Just imagine that alpha is current as current is the flow of positive charge.

Then use Fleming's left hand rule and find the direction of the motion:

1. The thumb is the deflection direction

2. The index is the direction of the magnetic field(in or out of the page).

3. The middle finger is the direction of the alpha particle.

So to find beta decay, always remember that beta deflects in the opposite direction of alpha particles and also by a larger angle

Elementary particles

All things are made from the smallest indivisable particles known as elementary particles

You will only need to know these particles:



• Quarks

There are 6 types of quarks and you need to remember them all but, there is an easier way to remember there charges

Charge = +2e/3	Up Quark	Charm Quark	Top Quark
Charge = -1e/3	Down Quark	Strange Quark	Bottom Quark

So what this table shows us that the particles in the first row have the same charge of +2e/3 where as the 2nd row has charges of -1e/3

Also remember that a quark has another similar but, opposite name like top and bottom quarks

Remember this table!




Protons and neutrons are made out of elementary particles called quarks



Remember that neutrons has 2 down quarks and 1 up quark

Remember that protons have 2 up quarks and 1 down quarks

If you do forget, use this method below!

Charge of a proton is +1e

+1e = 2e/3 +2e/3 - 1e/3

So we can find the number of up and down quarks



• Electron and Neutrinos

An electron is considered to be an elementary particle but, there are many types of electrons(actually 3 types):

1. Muon

2. Tau

3. Electron

They all have the same charge but, we only need to know electrons




And for each particle there is a corresponding neutrino

1. Muon Neutrino

2. Tau Neutrino

3. Electron Neutrino

Mostly, we talk about electrons and the electron neutrinos in beta decay only.

Also, Neutrinos are considered to be massless and chargeless so they don't affect the decay equation but, must be still added. This is because, it still carries a very little energy



• Photons

These are known to be called gamma photons as they are responsible for gamma radiation. Actually, gamma radiation are not just waves. According to Heinsberg's uncertainty principle, waves could be particles at the same time.

This radiation is responsible for pair production and annihilation of antimatter and matter




Antiparticle

So for each elementary particle, you have seen there is a corresponding antiparticle which has the same mass but, Opposite charge and spin. When representing them we put a dash above the original symbol

We will give some examples

Charge = -1	Electron
Charge = +1	Positron

We will also check the antiparticle of neutrinos

Charge = 0	Electron Neutrino	In beta(+) decay
Charge = 0	Electron antineutrino	In beta(-) decay

Also the antiparticle has the opposite properties

Classes of Particles

Particles can be classified into 2 main groups



• Hadrons

These are large particles such as protons and neutrons and are made out of quarks

These particles are affected by strong nucleur force and the weak forces. Actually all types of forces.

Hadrons can be divided in two more groups

• Baryons

These are particles which contain 3 quarks together

For example the proton - uud

• Mesons

These contains 2 quarks together. Usually an antiquark and a quark

These includes phi+ meson - up quark and antidown quark

We will need to know one more thing. The baryon number in an equation is always conserved and antiparticles have the opposite baryon number. But more information is not necessary...



• Leptons

These are electrons and neutrinos and their antiparticle

These particles are affected by all other forces except the strong nucleur force




The below part is not necessary but, it can help you with identifying if a neutrino or antineutrino is produced

During decay, the lepton number is conserved. The antiparticles have the opposite properties, which means that an antineutrino and a positron has a lepton number of -1 whereas, neutrinos and electrons have a lepton number of 1



So on the left side, it only contains neutrons and protons. It has no leptons so it is 0. On the right side, it has a electron with a lepton number 1 and another lepton must be present which is a antineutrino of lepton number -1 to cancel the other lepton and equate to 0

0 = +1-1




Fundamental Forces

There are 4 forces which govern the universe:

• Gravitational Force

Forces between masses

This is the weakest force in the universe but, it also has the largest range. In fact, the range is said to be infinite!

• Strong Nucleur Forces

Attraction forces which holds up the positive nucleus together. As the nucleus is made out of protons - positively charged. The strong nucleur force overcomes the repulsion forces between the protons.

You will need to know some details of this force:

1. This is the strongest force in the universe

2. This doesn't affect leptons but, only Hadrons and Quarks.

3. This force is highly short ranged and doesn't extend to the outer shell of an atom.

• Weak interaction or Weak force

All you have to know is that this force is necessary for both types of beta decay as we have seen it changes neutrons to protons



To change the identity, this force is required. So this is not technically a force but, an interaction

• Electromagnetic Force( Electrostatic force )

These are forces between charged objects. Anything that has a charge, creates an electric field around it and causes other charges to experience a force




Annihilation



When a particle and the corresponding antiparticle meets, they annihilate and release energy in the form of Gamma radiation or two gamma photons

So Momentum, charge and mass-energy is conserved




Pair Production

This is the reverse of annihilation.

When a Gamma ray is passed through a nucleus, a particle and the antiparticle is formed. The nucleus is essential to conserve momentum.




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