Radioactive Decay: An Introductionardent.web.cern.ch/ardent/dl/outreach/Introduction to Radioactive...

RADIOACTIVE DECAY:

AN INTRODUCTION

The atom

• All matter is made up

of positive Protons,

negative Electrons and

neutral Neutrons

• Protons and Neutrons

form the nucleus, and

electrons orbit in

discrete energy levels

• This becomes important

when we talk about

interactions with radiation

11/26/2013 Radioactive Decay: An Introduction 2

The atom

• Atoms with different

numbers of neutrons

are called ‘isotopes’ • For Example: 3He and 4He

are isotopes of Helium, with

1 and 2 neutrons respectivly


Electric Fields

• An electric field is created by

differences in ‘potential’ between

two points

• A potential is a build up of

charge, and will either attract or

repel objects that also have a

charge

• An example of this is a battery:

the positive terminal has a build

up of positive charge, and vice

versa


Coulomb’s Law

• 𝐹 = 𝑘𝑒𝑞1𝑞2

(𝑟2,1)2 𝑟 2,1

• where ke is Coulomb’s constant, q1

and q2 are the 2 different charges,

r2,1 is the distance between them

and 𝑟 2,1 is the unit vector from

charge 2 to 1


The Atom (2)

• An ‘Ion’ is an atom that

does not have a neutral

charge: one with either

more or less electrons

than protons

• In this image, d. is an

Ion, as it has one less

electron than proton,

giving it a charge of +1 e


The Atom (2)

• Radiation can ionize an atom by giving enough energy to an electron: there is a threshold to this process however

• The threshold for this process is dependent on the number of protons in the nucleus squared:

• 𝐸 = −𝑍213.6

𝑛2𝑒𝑉; where Z is the

atomic number, and n is the orbital number

• Electron volts (eV) is a unit of energy, with 1 eV being the amount of energy given to 1 electron accelerated by a potential of 1 Volt

• 1 eV = 1.6 10-19 J


Magnetic Fields

• Magnetic fields are set up

by two different ‘Poles’:

North and South (Nord e

Sud)

• They can also be created

by moving charge (current)

• Vice Versa, a changing

magnetic field creates an

electric field


Electromagnetism

• Q. So, it can be seen that electic fields and magnetic

fields are related, by why do we care?

• A. Electromagnetism is fundamental for radiation!

• Some radiation interacts through electromagnetic forces,

and others are completly ‘made-up’ of electromagnetic

fields


What is Radiation?

• Particles that carry energy

• Most common can be split into 2 categories: • Charged: Protons, electrons, alpha particles and heavy ions

• These particles have an electrical charge; this is how they transfer the energy

to matter

• These particle carry energy through momentum (Kenetic energy)

• Uncharged: Photons (also known as X rays, Gamma rays or even

visible light) and neutrons

• These have no electrical charge, and transfer energy by collisions or

absorption by matter

• Photon’s energy is a function of their wavelength; they have no rest mass and

therefore no Kenetic energy (this is not strictly correct, but a convenient

explanation)


Electrons

• Also known as ‘Beta radiation’

• Lose energy by interacting with the electric field around

the atoms making up an object (coulomb interaction)


Electrons

• Collisional Losses • The electron transfer energy to the

material through coulomb interaction

• Radiation Losses • The electron can emit electromagnetic

radation along its path (that is, photons)

• One of these processes is known as

Bremsstrahlung radiation, where the

radiation is emitted while the electron is

being decelerated by a nucleus


Protons/Ions

• Protons, Alpha particles (ionised Helium atoms) and heavy ions

interact with matter in the same way – through the coulomb

interaction

• They lose energy continuosly as they move through matter

• These heavy ions have a straight path, unlike electrons,

because they have a much larger mass


Protons/Ions

• These particles lose energy in a way that is unique: they lose most of their energy at the end of their track

• As the particle slows, it is affected more by the electric field inside the material: this is because it spends more time close to each atom

• The amount of energy that is transfered per distance travelled is called the stopping power; it is dependent on the material and the particle energy

• When plotted, this is called the Bragg peak


Uncharged Radiation

• Uncharged: Photons and Neutrons

• These particles do not have a net electrical charge so they must interact

with the target matter directly

• We will not deal with neutrons: they are complicated and will not be

involved with the experiment

= +


Photons

• Photons are electro-magnetic waves that travel at the

speed of light (because that is what they are)

• Photons are characterised by 2 main properties: • Wavelength

• Frequency


Photons

• The frequency and

wavelength are

related by the

formula: f λ = c;

where c is the speed

of light (around 3 ×

108 m/s)

• As the energy of the

photon increases, so

does the frequency

(or time for photons)


Photons


2 x 10-24 J 2 x 10-22 J 5 – 3 x 10-19 J 2 x 10-17 J 2 x 10-14 J

1.25 x 10-5 eV 1.25 x 10-3 eV 3.1 – 1.87 eV 125 eV 1.25 x 105 eV

• 1 eV = 1.6 10-19 J

Ionisation

energy

Photons

• The way that photons interact with matter is to be absorbed or scattered

• ‘Compton scattering’ is when a photon scatters off an electron, and gives some energy to electron

• For ‘Rayleigh scattering’, the photon strikes a nucleus instead of an electron

• Otherwise, the photon can be completely absorbed • If the energy of a photon striking an

electron is enough to free the electron, it is called the ‘Photoelectric effect’, and this electron is now radiation as well!


Photons

• ‘Pair Production’ can only occur when a photon has an energy

of more than 1022 KeV, and is when it spontaneously devolves

into an electron and a positron


Photons

• Put together, these processes mean that the intensity of photon radiation follows this relation:

•𝐼

𝐼0= 𝑒−

𝜇𝜌 𝜌𝑡

• Where I0 is the initial intensity (number of photons per unit area), I is the intensity at a thickness t, ρ is the desity of the material and (μ/ρ) is the mass attenuation coefficient

• (μ/ρ) is the probability of a photon being absorbed (made up of the probablility of a photoelectric, Compton or pair production interaction) divided by the density of the material


Decay

• ‘Radioactive decay’ is what

happens when nucleus is in an

excited state, and must release

energy

• Decay cannot happen at any

time for ‘stable’ atoms: there is

a ‘binding energy’, which is

what holds the nucleus

together -> this must be

overcome in order for the

nucleus to release radiation


Decay

• Certain isotopes are unstable, due to a combination of

energy levels and the strong/weak nuclear force

• Radon is a naturally unstable element, with the most

stable isotope (222Rn) having a half-life of 3.8 days

• The ‘activity’ of a radioactive source is measured in

Becquerel (Bq), which is one decay per second


Decay

• In order to understand this, you

need to know that the nucleus

does not have a set energy, only

a probability of having a particular

energy

• Therefore there is a possibility

that the nucleus to tunnel to a

lower energy state

• Naturally unstable nuclei are

outside the well even at their

lowest energy, so they must

decay to become stable


Decay

• The decay law describes the rate at which the material

decays

• It is an exponential relation between the number of

undecayed atoms and time

• Mathematically, this is shown as:

• 𝑁𝐴 = 𝑁𝐴0𝑒−λ𝑡 ;here NA is the number of atoms at time t, NA0 is

the initial number of atoms and λ is the decay

constant

• The half-life of the isotope is defined as the time in which

half of the total atoms decay (when NA/NA0 = 1/2):

• 𝑡1/2 = −1

λ𝑙𝑛

𝑁𝐴

𝑁𝐴0= −

1

λ𝑙𝑛

1

2=

1

λ𝑙𝑛 2


Decay

• When a nucleus decays, it is called

a ‘parent’ before the decay and a

‘daughter’ afterwards

• When a nucleus decays into

another unstable nucleus, and

then continues decaying, this is

called a decay chain


Thank you for listening!

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