This presentation provides notes about radioactive decay for IB Physics students

1. Radioactive Decay

2. Alpha Decay (α)
An alpha particle is emitted from the nucleus and the
decaying nucleus turns into a different nucleus.
E.g. Uranium undergoes alpha decay and turns into Thorium
Experiment by Rutherford and T. Royd shown that α
particles are identical to the nuclei of Helium. The gas
produced by α particles was collected by the scientist after
investigation they found that the spectrum of gas was
identical to the helium gas.

3. Beta Decay (β)
In beta minus decay, a neutron in a decaying nucleus turns
into a proton, an electron and an anti-neutrino emits.
E.g. Thorium undergoes beta minus decay and turns into
the nucleus of protactinium
In beta plus decay, the nucleus emits an anti-particle
known as a positron (positively charged) and a neutrino.
E.g. Sodium undergoes beta plus decay and turns into the
nucleus of Neon

4. Gamma Decay (γ)
In gamma decay, a gamma ray is emitted from the nucleus,
it is a photon of high-frequency electromagnetic radiation.
In gamma decay, the nucleus does not change its identity. It
only moves from a higher to lower nuclear energy level.
The wavelength of the emitted photon is given by
λ =
ℎ𝑐
𝐸

5. Properties of alpha, beta and gamma rays

6. Decay Series
In physics, a radioactive decay chain is a sequence of unstable atomic nuclei and
their modes of decay, leading to a stable nucleus. Sources of these unstable nuclei
are different, but engineers mostly deal with naturally occurring radioactive decay
chains known as radioactive series.
A radioactive nucleus such as thorium (Z=90) decays first by alpha decay into the
nucleus of radium (Z=88). Then radium, which is also radioactive, decays into
actinium (Z=89) by beta decay. Further decays will take place until the resulting
nucleus is stable i.e. Lead (Z=82). The set of decays that takes place until a given
nucleus ends up as a stable nucleus is called the decay series of the nucleus.

8. The law of radioactive decay
It states that the rate of decay is proportional to the number of
nuclei that have not decayed yet
Δ𝑁
Δ𝑡
α N
Half Life
It is the interval of time after which the activity of
a radioactive sample is reduced by a factor of 2

9. For example:
Initially there are 1.6 x 1022
𝑛𝑢𝑐𝑙𝑒𝑖 𝑜𝑓 𝑡ℎallium at (t=0) with
a mass of about 6g.
After 3 minutes, there are 0.8 x 1022 nuclei of thallium
After another 3 minutes, there are 0.4 x 1022 nuclei of thallium
Then after 3 more minutes, there are 0.2 x 1022 nuclei of thallium
Here, the time of 3.0 minutes would be the Half Life of the
thallium.

10. Activity or Decay rate:
The number of decays per second.
The unit of decay is becquerel (Bq)
i.e. 1 Bq is equal to 1 decay per second.

13. Unified Atomic Mass Unit
The unified atomic mass unit (u),is a unit of atomic and
molecular mass. By definition it is one twelfth of the mass of
an unbound carbon-12 (12C) atom, at rest and in its ground
state.
1u = 1.6605402x 10−27Kg

14. The Mass Defect
A mass defect is the difference between an atom's mass and the sum of
the masses of its protons, neutrons, and electrons. The reason the
actual mass is different from the masses of the components is because
some of the mass is released as energy when protons and neutrons bind
in the atomic nucleus.
• Protons and neutrons are very tightly bound to each other in a
nucleus. To separate them, energy must be supplied to the nucleus.
• Conversely, energy is released when a nucleus is assembled from its
constituent nucleons.
• From Einstein's theory of relativity, energy E is equivalent to mass m
according to the equation “E=m𝑐2”.
• Since energy is released when nucleons are brought together to form
a nucleus, this is equivalent to a loss of mass.
• So the mass of the constituent nucleons when far part is greater than
the mass of the nucleus

15. Take the nucleus of helium (A=4, Z=2), as an example. The mass of an atom of
helium is 4.0026u.
This includes the mass of two electrons.
So the nuclear mass is Mnucleus = 4.0026 - 2×0.0005486
Mnucleus = 4.0015 u
The helium nucleus is made up of two protons and two neutrons. Adding these
masses we find:
2m(p)+2m(n) = 4.0319 u
This is larger than the mass of the nucleus by 0.0304 u, which is as expected.
This leads to the concept of mass defect.

16. Binding Energy
The energy equivalent to the mass defect is called binding energy. The
binding energy of a nucleus is the work (energy) required to completely
separate the nucleons of that nucleus.
The work required to remove one nucleon from the nucleus is very
roughly the binding energy divided by the total number of nucleons.
At a more practical level, the binding energy per nucleon is a measure of
how stable the nucleus is - the higher the binding energy per nucleon,
the more stable the nucleus.

17. The Binding Energy Curve

18. How to find the energy that corresponds to 1 u:

19. Energy released in a decay
Δm = total mass of reactants – total mass of product
• If Δm is positive then energy will be released and the decay will occur.
• If Δm is negative the reactants will not react and the reaction can only
take place if energy is supplied to the reactants.

20. Consider the reaction in which an alpha particle collides with a nucleus of nitrogen
Note that the sum of the atomic and mass numbers on both sides of the reaction are
equal.
This is a famous reaction called the transmutation of nitrogen; it was studied by
Rutherford in 1909.
In this reaction the mass difference is negative:
Δm=18.005677-18.006956Am -0.00128 u
This reaction will only take place if the alpha particle has enough kinetic energy to
make up for the difference.
The minimum kinetic energy needed is 0.00128 × 931.5=1.2 MeV..

21. Nuclear Fission Reaction
It is the process in which a heavy nucleus splits up into lighter nuclei.
When a neutron is absorbed by a nucleus of uranium-235, uranium
momentarily turns into uranium-236. It then splits into lighter nuclei
plus neutrons. One possibility is
This is a fission reaction.
The production of neutrons is a feature of fission reactions. In a reactor,
the neutrons released can be used to collide with other nuclei of
uranium-235, producing more fission, energy and neutrons.
The reaction is thus self-sustaining - it is called a chain reaction.
For the chain reaction to get going a certain minimum mass of uranium-
235 must be present, otherwise the neutrons escape without causing
further reactions - this is called the critical mass.

22. The energy released can be calculated as follows:
Δm = 236.0526u - (143.92292 + 88.91781 + 3 x 1.008665) u
= 0.185875 u
For this reaction
Q = Δmc² = 0.185875 x 931.5 = 173 MeV approx.
This energy appears as kinetic energy of the products.
The energy can be released in a controlled way, as in a fission reactor or in a very short
time, as in a nuclear explosion.
Note that the fission process is an induced process and begins when a neutron collides
with a nucleus of uranium-235.
Spontaneous fission, i.e. a nucleus splitting into two roughly equal nuclei without
neutron absorption, is possible for some heavy elements but is rare.

23. Nuclear Fusion Reaction
It is the joining of two light nuclei into a heavier one with the associated
production of energy.
An example of a fusion reaction is:
In this reaction two deuterium nuclei (isotopes of hydrogen) produce
helium-3 (an isotope of helium) and a neutron.
From the mass difference for the reaction, we can work out the energy
released:
Δm = 2 × 2.014102 - (3.016029 + 1.008665) u
Δm = 0.0035 u
Therefore: Q = Δmc² = 0.0035 x 931.5 = 3.26 MeV

25. Fission reaction or Fusion reaction ?
We have already seen that fission occurs when heavy nuclei split up and
fusion when light nuclei fuse together. This becomes easier to
understand when we look at the curve of binding energy per nucleon
against nucleon number. The dashed vertical line at nickel-62 in Figure
7.15 is at the peak of the curve this is the most energetically stable
nucleus. To the left, nuclei can become more stable by fusion, while to
the right they become more stable by fission.

26. • The electron was discovered in 1897
• The nucleus in 1911
• The proton in 1920
• The neutron in 1932, by the 1930s we had all the
ingredients of matter.
• The photon had been known since 1905.
• The neutrino, which features in beta decay, was
hypothesized to exist in 1930 and was discovered in 1956.
• Hundreds of other particles were discovered in cosmic ray
experiments. In particle accelerators around the world,
collisions between high-energy electrons or protons
produced hundreds of new, unknown particles.
• In a device known as the bubble chamber, charged
particles left a trace of their path that could be
photographed and analysed. The reason these particles
are not found in ordinary matter is that they are very
unstable and decay very quickly.
• A few of these are the pions, the kaons, the etas, the
hyperons, and hundreds of others. These particles decay
with half-lives ranging from .

27. There are three classes of elementary particles:
The quarks, the leptons and the exchange particles.
Quarks
Murray Gell-Mann (born 1929) and Georg Zweig (born 1937) Quarks were first
to propose Quarks.
There are six different types or flavours of quarks
• the up (u),
• charm (c)
• top (t) quarks with electric charge e
• the down (d),
• strange (s)
• bottom (b) quarks with electric charge-je.
• Top and bottom quarks are alternatively called truth and beauty.
• There is solid experimental evidence for the existence of all six flavours of
quarks. Then there are anti-particles of each of these with same mass but
all other properties are opposite.
• Anti-particles are denoted with a bar on top of the symbol for the name.
Quarks combine in just two ways to form other particles called hadrons.

29. Pions are examples of mesons. The positively charged pion (π + meson) is made up as
follows:
π + = ( uđ )
The bar over the 'd' shows this is an anti-particle. Thus, the positive pion is made out of a
u quark and the anti-particle of the d quark.
Quarks have another property called baryon number, B. Each quark is assigned a baryon
number of + and each anti quark a baryon number of –
To find the baryon number of the hadron that is formed by quarks, just add the baryon
numbers of the quarks in the hadron.
For example:
uct baryon number = +⅓+ ⅓ + ⅓ = +1 (a baryon)
uđ baryon number = + ⅓ - ⅓ = 0 (a meson)
Since all baryons are made from three quarks, all baryons have baryon number +1.
All anti-baryons have baryon number -1 and all-mesons have baryon number 0.
(Note that all other particles not made from quarks also have a baryon number of 0.)
Quarks interact with the strong nuclear interaction, the weak nuclear interaction and the
electromagnetic interaction.

30. Lepton:
There are six types of lepton, electron and its neutrino, the
muon and its neutrino, and the tau and its neutrino.
• The muon is heavier than the electron, and the tau is
heavier than the muon.
• There is now conclusive evidence that neutrinos have a
very small non-zero mass.
• We have the anti-particles of these.
• All leptons interact with the weak nuclear interaction.
• Leptons are assigned a new quantum number called
family lepton number. There is an electron, muon and
tau lepton number.
• The family lepton number is conserved in all interactions

31. Exchange Particle:
An interaction between two particles is the exchange of a
particle between them. In electromagnetic interaction the
particle exchanged is a photon.
One electron emits the photon and the other absorbs it.
The emitted photon carries momentum and so the electron
that emits it changes its momentum, i.e. experiences a force.
Similarly, the particle that absorbs the photon changes its
momentum thus also experiencing a force.
The other interactions are also described in terms of
exchange particles.
Confinement:
Quarks only exist within hadrons. This has led to an important principle, that of quark
confinement.
It is not possible to observe isolated quarks.
Suppose that one attempts to remove a quark from inside a meson. The force between
the quark and the anti-quark is constant no matter what their separation is, so the total
energy needed to separate the quark from the anti-quark gets larger and larger as the
separation increases. If one insisted on providing more and more energy in the hope of
isolating the quark, all that would happen would be the production of a meson-anti-
meson pair and not free quarks.

32. Higg’s Particle:
The theory of quarks, leptons and exchange particles defines what is now called the
Standard Model of particles and interactions.
All aspects of this model except one have been verified experimentally long ago.
The missing link was the existence of the Higgs particle: a neutral particle required to
exist by the theory of the standard model.
The Higgs particle is responsible, through its interactions, for the mass of the
particles of the standard model, in particular the masses of the W and the Z.