Nuclear Physics

Physics 12

Protons, Neutrons and Electrons

The atom is composed of three subatomic particles:

ParticleCharge(in C)

SymbolMass

(in kg)

Electron -1.602x10-19 e- 9.109 56x10-31

Proton 1.602x10-19 p+ 1.672 614x10-27

Neutron 0 n0 1.674 920x10-27

Atomic Nucleus Atom described

using: X – atomic symbol A – atomic mass

number (nucleon number)

Z – atomic number Number of protons

and electrons = Z Number of

neutrons = A - Z

AZX

Strong Nuclear Force

The electrostatic forces inside a nucleus would rip it apart if there was not another force

By the end of the 1930’s physicists had determined that nucleons attract each other

This is the strongest force in the known universe

Stability and the Nucleus Although the Strong Nuclear Force is

strong enough to hold a small nucleus together, as the size of the nucleus becomes larger, the electrostatic forces begin to become more important

As a result, if we consider various nuclei based on their Atomic Number and Neutron Number we get the following result:

Stability and the NucleusEach black dot represents a stable nucleus, with the number of neutrons shown on the vertical axis and the number of protons on the horizontal axis

Nuclides and Isotopes

Nuclides are different combinations of nucleons

Isotopes occur when an element (specific Atomic Number) has different numbers of neutrons (different Atomic Mass Numbers)

For example, there are three common isotopes of hydrogen:

Nuclides and Isotopes

Nuclear Binding Energy

It takes 13.6 eV to separate an electron from a hydrogen atom

However, it takes more than 20 MeV to separate a neutron from a helium-4 atom

The energy to separate all the nucleons in a nucleus is called the binding energy

Larger nuclei are held together a little less tightly than those in the

middle of the Periodic Table

Mass Defect If you were able to apply the 20 MeV required to

separate a neutron from helium-4, what would happen to it?

This is dealt with using Einstein’s Special Theory of Relativity and the fact that mass and energy are equivalent E = mc2

The mass of helium-4 (2p, 2n) is smaller than that of helium-3 (2p, 1n) and a neutron

The energy that was added to remove the neutron was converted into mass

The difference between the mass of a nuclide and the sum of the masses of its constituents is called mass defect

Atomic Mass Unit (u) When dealing with nucleons, it is often

more useful to deal with mass in unified atomic mass units (u) instead of kilograms

ParticleMass

(in kg)Mass(in u)

Electron 9.109 56x10-31 0.000 549

Proton 1.672 614x10-27 1.007 276

Neutron 1.674 920x10-27 1.008 665

Binding Energy Example

Determine the binding energy in electron volts and joules for an iron-56 nucleus given that the nuclear mass is 55.9206u

55.9206

56

26

30

nucleusm u

A

Z

N A Z

N

Binding Energy Example

Determine the binding energy in electron volts and joules for an iron-56 nucleus given that the nuclear mass is 55.9206u

26(1.007276 ) 30(1.008665 )

56.449126

56.449126 55.9206

0.5285

total p n

total

total

m Zm Nm

m u u

m u

m u u

m u

Binding Energy Example

We would expect the binding energy per nucleon to be about 8MeV:

2

8 2

11

11

19

8

0.5285 (3.00 x 10 / )

7.888 10

7.888 10

1.602 10 /

4.924 10

E mc

E u m s

E x J

x JE

x J eV

E x eV

864.924 10

8.79 1056

x eVx eV

Radioactive Isotopes

In discussing the nucleus, we looked at a plot of stable nuclei

It is also possible to have a nucleus that is not stable (meaning that it will fall apart)

An unstable nucleus will decay following a few very specific processes

We call this decay radioactivity and classify it into one of three types

Radioactive Isotopes

Alpha Decay An alpha particle (α) is a helium nucleus

(two protons and two neutrons) A nucleus that emits an alpha particle will

lose the two protons and two neutrons Large nuclei will emit alpha particles They do not penetrate matter well and a

sheet of paper or 5cm of air will stop most They can free electrons from atoms,

meaning they are a form of ionizing radiation

Alpha Decay

Beta Decay When a nucleus emits a beta particle

(β), it appears to lose an electron or positron from within the nucleus

There are two types of beta decay (β- and β+)

Beta particles can penetrate matter to a greater extent than alpha particles; they can penetrate about 0.1mm of lead or 10m of air

They are also a form of ionizing radiation but less damaging than alpha particles

Beta Decay (β-) In this type of beta decay, a neutron

becomes a proton and a β- particle (high energy electron) is emitted

In addition an antineutrino ( ) is emitted (antimatter) along with the beta minus particle

The nucleus’s atomic number increases by one while the atomic mass number remains the same

Beta Decay (β-)

Beta Decay (β+) In this type of beta decay, a proton

becomes a neutron and a β+particle (high energy positron or antielectron) is emitted

In addition a neutrino ( ) is emitted along with the beta plus particle

The nucleus’s atomic number decreases by one while the atomic mass number remains the same

Beta Decay (β+)

Gamma Decay (γ) When a nucleus goes through alpha or

beta decay, the daughter nucleus is often left in an excited state

In order to reduce the energy of the nucleus, it will go through gamma decay (high energy photon) to return to the ground state

Gamma radiation can pass through 10cm of lead or 2km of air

It is the most damaging of all due to the energy of the gamma particle

Gamma Decay

Decay Series

When a large nucleus decays by alpha and beta radiation, the daughter nucleus will be more stable than the original nucleus

However, the daughter nucleus may still be unstable and will itself go through alpha or beta radiation

This leads to a decay series

Rate of Radioactive Decay It is impossible to predict when a specific

nucleus will decay You can describe the probability of decay The concept of half life is used with

radioactive decay: the time required for half of the sample to decay

Using the half life equation, it is possible to determine how much of a sample would remain after a given period of time

Half Life

N sample remaining N0 original sample Δt elapsed time T half life

0

1

2

tT

N N

Half Life