Basics Of Nuclear Physics

By

Muhammad Zeeshan Khalid

The Atom

The atom consists of two parts:

1. The nucleus which contains:

2. Orbiting electrons.

protonsneutrons

All matter is made up of elements (e.g. carbon, hydrogen, etc.).

The smallest part of an element is called an atom.

Atom of different elements contain different numbers of protons.

The mass of an atom is almost entirely due to the number of protons and neutrons.

The Atom

XA

Z

A = number of protons + number of neutrons

Z = number of protons

A – Z = number of neutrons

Number of neutrons = Mass Number – Atomic Number

Binding Energy

• The missing energy that keeps the nucleus together

Mass Of Atom 1.007825 u

+ Mass of neutron +1.008665 u

__________________ __________

Expected Mass of atom 2.016490 u

The mesasurd mass of = 2.014102 u So the difference is 0.002388 u

11H

21H

21H

(0.002388 )(931.48 / ) 2.224E u Mev u Mev∆ = =

The binding energy of an atom is the energy released as all the constituent particles (n, p and e) come together FROM INFINITY under both the STRONG force and the EM force.

The binding energy is something that is LOST from the atomic system. Thus it is not something that the system possesses.

CONCEPT OF BINDING ENERGY

CALCULATION OF BINDING ENERGY

Total Energy Total Energy

( ) ( ) EBcXcZmNmZm Nenp . M 2AZ

2 +≡++

( ) ( )( )( )

( ) 2

2

22

atom mass - tsconstituen mass

Z .

c

cXMNmZm

cXMcZmNmmEBAZnH

NAZenp

=

−+=

−++=

ANOTHER WAY OF VIEWING BINDING ENERGY

+

ATOM Constituents at infinity

The opposite way of seeing binding energy - is that if B.E. (MeV) is put into the atom then there is just enough energy available to split all the constituents of the atoms apart and get them to rest at infinity.

SINGLE NEUTRON SEPARATION ENERGY

The same method can be used to easily compute the “Single Neutron Separation Energy” – which is the energy required to “pull” a neutron out of the nucleus.

( ) ( )

( ) ( )[ ] 21

1

221

12

MM

M M

cXmXS

cmcXcXS

NAZnN

AZn

nNAZN

AZn

−+=

+≡+

−−

−−

Note we don’t have to measure Sn directly.

SINGLE PROTON SEPARATION ENERGY

The same clever strategy applies to finding the “Single Proton Separation Energy” Sp. But note here there is a difference – we must be careful in counting electron mass.

( ) ( ) 22211

2 M M cmcmcYcXS epNAZN

AZp ++≡+ −

−

( ) ( )[ ]( ) ( )[ ] 21

1

211

MM

MM

cXmY

cXmmYS

NAZHN

AZ

NAZepN

AZp

−+=

−++=−−

−−

=pS [Mass of Final Products – Mass of Initial atom] c2

THE FAMOUS B/A (binding energy per nucleon) CURVE

Isotopes

• Isotopes are variants of a particular chemical element such that, while all isotopes of a given element have the same number of protons in each atom, they differ in neutron number.

U235

92U

238

92

There are many types of uranium:

Isotopes of any particular element contain the same number of protons, but different numbers of neutrons.

A 235

Z 92

Number of protons 92

Number of neutrons 143

A 238

Z 92

Number of protons 92

Number of neutrons 146

Most of the isotopes which occur naturally are stable.

A few naturally occurring isotopes and all of the man-made isotopes are unstable.

Unstable isotopes can become stable by releasing different types of particles.

This process is called radioactive decay and the elements which undergo this process are called radioisotopes/radionuclides.

Radioactive Decay

• Radioactive decay, also known as nuclear decay or

radioactivity, is the process by which a nucleus of an unstable

atom loses energy by emitting particles of ionizing radiation.

A material that spontaneously emits this kind of radiation—

which includes the emission of energetic alpha particles, beta

particles, and gamma rays—is considered radioactive.

Radioactive decay results in the emission of either:

• an alpha particle (α),

• a beta particle (β),

• or a gamma ray(γ).

Radioactive Decay

An alpha particle is identical to that of a helium nucleus.

It contains two protons and two neutrons.

Alpha Decay

XA

ZY

A - 4

Z - 2+ He

4

2

Alpha Decay

unstable atom

more stable atom

alpha particle

Alpha Decay

Ra226

88

Rn222

86

He4

2

Beta Decay

Beta decay is one process that unstable atoms can use to become more stable. There are two types of beta decay, beta-minus and beta-plus.

During beta-minus decay, a neutron in an atom's nucleus turns into a proton, an electron and an antineutrino.

Beta Decay

During beta-plus decay, a proton in an atom's nucleus turns into a neutron, a positron and a neutrino.

Gamma Decay

Gamma rays are not charged particles like α and β particles.

Gamma rays are electromagnetic radiation with high frequency.

When atoms decay by emitting α or β particles to form a new atom, the nuclei of the new atom formed may still have too much energy to be completely stable.

This excess energy is emitted as gamma rays (gamma ray photons have energies of ~ 1 x 10-12 J).

The activity of a radioactive sample is the rate at which atoms decay.

If N(t) is the number of atoms present at a time t, then the activity R is

dN/dt is negative, so the activity is a positive quantity.

dNR = - .dt

The SI unit of activity is the becquerel: 1 becquerel = 1 Bq = 1 event/second.

Another unit of activity is the curie (Ci) defined by1 curie = 1 Ci = 3.70x1010 events/s = 37 GBq.

12.2 Half-Life

Experimental measurements show that the activities of radioactive samples fall off exponentially with time.

*Empirically:-λt

0R = - R e .

*Argh!

λ is called the “decay constant” of the decaying nuclide. Each radioactive nuclide has a different decay constant.

The half- l i fe, T½, is the time it takes for the activity to drop by ½. We can find a relationship between λ and T½:

original activityactivity after T½

1/2-λΤ00

R = -R e2

1/2-λΤ1 = e2

1/2+λΤe = 2

( )1/2Τ = ln 2 λ

( )1/2 1/2

ln 2 0.693 = =Τ Τ

λ

Here's a plot of the activity of a radionuclide.

The initial activity was chosen to be 1000 for this plot.

The half-life is 10 (in whatever time units we are using).

Al l decay curves look like this; only the numbers on the axes will differ, depending on the radionuclide (which determines the half-life) and the amount of radioactive material (which determines the initial activity).