nuclear binding energy
TRANSCRIPT
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).