Download Atomic Models

Atomic nuclei and radioactivity
Yeh, Chien-Yi
Medical Physics Section
Radiation Oncology Department
Chung-Gung Memorial Hospital at Lin-kuo
Structure of Matter
1803, Dalton :proposed the atoms having characteristic weight.
The word atom was derived from Greek atomos, meaning
“indivisible”. However as we know today, atoms are composed
of smaller particles such as electrons, protons, and neutrons.
Matter
Water
Element
Atom
H2O
H, O
10-10m
Atomic Models
1897, a British physicist Sir J.J. Thomson
Discovery the atom as having electrons
moving in constant motion inside a positively
charged medium. It is often referred to as
the
plum
pudding
model.
1914, Ernest Rutherford proposed that
electrons revolve around a massive positively
charged nucleus in an atom like the planets
revolving around the sun in the solar system.
This Rutherford model was derived from the
experiment in which a thin gold foil was
bombarded with high-energy alpha particles.
Scattering Experiment
Atomic Models
The nucleus of an atom composes of two subatomic particles,
the protons and the neutrons. Rutherford discovered the
proton in 1914 while James Chadwick discovered the neutron
in 1932. Thus far, atoms are found to compose of three
subatomic particles, electrons, protons, and neutrons.
Electron: e = 1.602 x 10-19 C and a mass of about 9.109 x 10-31 kg.
Proton: e = 1.602 x 10-19 C and a mass of about 1.6726 x 10-27 kg.
Neutron: a mass of about 1.6747 x 10-27 kg.
Distribution of orbital electrons
Bohr (1913)
1) electrons revolve around the nucleus in definite orbits corresponding
to definite energy states.
2) whenever an electron jumps from a higher energy state to a lower
energy state, a photon having an energy equals to the energy
difference between the two energy states is emitted.
Erwin Schrodinger (1887-1961) and Werner Heisenberg (1901-1976)
independently developed a new theory called quantum mechanics.
The assignment of various quantum numbers to an electron is quite simple
but to a multi-electron atom can be very difficult. This classification of
electrons became clear when Wolfgang Pauli (1900-1958) formulated the
Pauli exclusion principle. The Pauli exclusion principle states that “No two
electrons in the same atom can have identical set of quantum numbers”.
Quantum mechanical rules and the Pauli exclusion principle govern the
arrangement of electrons in an atom.
Erwin Schrödinger
in Vienna
Werner Heisenberg
In Würzburg.
Wolfgang Pauli
in Vienna
Under the present atomic model, electrons are described as revolving in definite
orbits or shells through empty space around a centrally located massive
positively charged nucleus. There are many definite orbits available for the
electrons to occupy. These orbits are specified or identified using a set of
parameters called quantum numbers. Quantum numbers are special numbers
that are derived based on quantum physics. The word quantum is used to
describe the discrete nature instead of continuous nature of the orbits.
Quantum mechanics requires four different quantum numbers to specify
an energy state in an atom. The four quantum numbers are the
principal quantum number n, the orbital quantum number l, the
magnetic quantum number m, and the spin quantum number s.
n = 1, 2, 3 ...
l = 0, 1, 2 ... n-1
m = -l, ...0..., +l
s = +1/2 or -1/2
Atomic energy level
Quantum model
E = hv
E = hc/l
Plank’s constant = 6.62 X 10-34 J-S
E (joule) =
1.24 X 10-6 (j.s) (m/s)
l (m)
The Nucleus – composed of neutrons and protons
10-14m
mass number
A
Z
atomic number
X
Chemical symbol
called a nuclide
A
Z
A
X
mass number = the # of nucleons
= the sum of neutrons and protons
Z
atomic number = the # of protons
= the # of electrons outside the nucleus
Unit charge = 1.6X10-19 Coulombs
A
Z
X
Protons(Z)
Neutrons(A-Z)
Mass # (A)
Isotopes
Same
Different
Different
Isotones
Different
Same
Different
Isobars
Different
Different
Same
Isomers: the same composition of protons and neutrons,
but different nuclear energy state
A
Segre’s chart
N>P
For the short-range nuclei force
competes with Coulomb force
Z
X
Atomic mass and energy unit
1 atomic mass unit = 1/12 mass of
12
6
C
1 amu = 1.66 X 10 –27 kg
1 mole 12C = 12X10-3 kg
= 6.0228X1023 atoms 12C
Avogadro’s number NA = 6.0228 X 10 23
electorn = 0.000548 amu = 9.1 X 10-31 kg
proton = 1.00727 amu
neutron= 1.00866
For 4He = 4.0026 < 2X1.00727+2X1.00866 = 4.03186
Mass defect = 4.0026-4.03186 = -0.02926
Binding energy of nucleus = 0.02926 amu energy
Principle of equivalence of mass and energy
mass transfer to energy
E = mc2
E0 (rest energy of electron) = 0.511 MeV
9.1X10-31kgX(3X108m/s)2/1.602X10-13(J/MeV) = 0.511
1 amu = 931 MeV
1 eV = 1.602 X 10 –19 C X 1V = 1.602 X 10–19 J
Nuclear force
- strong nuclear force
- electromagnetic force
- weak nuclear force
- gravitational force
Electromagnetic radiation
EM wave – energy propagation like UV, X-ray, g-ray (from decay)
c = ul
Radioactivity
First discovered by Henri Becquerel in 1986, is a phenomenon in which
radiation is given off by the nuclei of the elements. It can be in the form
of particles, electromagnetic radiation, or both.The process of radioactive
decay or disintegration is a statistical phenomenon. It’s based on that the
number of atoms decay per unit time, (N/t) is proportional to the
number of radioactive atoms, (N) present.
N
N
N
= l N
t
t
N = N0e
 lt
No is the initial number of radioactive atoms

Activity
A = l N  A = A0e
 lt
•
The activity of a radioactive material is the rate of decay .
•
A is the activity remaining time t.
•
A0 is the original activity equal to lN0.
1 Ci = 3.7 x 1010 dps
1 Bq = 1 dps = 2.70 x 10-11 Ci
The half-life
The half-life is defined as the time required for either the
activity or the number of radioactive atoms to decay to
half the initial value.
T1/ 2 =
ln 2
l
=
0.693
l
The average life
It is the average lifetime for the decay of radioactive atoms.
Ta = 1.44T1/ 2
Radioactive equilibrium
A 2 = A1
l2
l2  l1
(1  e ( l2 l1 )t )
Transient equilibrium
COW
For a time period t>>l2
A 2 = A1
l2
l2  l1
l2
= A1
l2  l1
(1  e ( l2 l1 )t )
MILK
Secular equilibrium
For a time l2 >> l1
A 2 = A1
l2
l2  l1
(1  e ( l2 l1 )t )
= A1 (1  e l2t )
= A1
Modes of radioactive decay
•
•
•
•
•
 particle decay
 particle decay
Electron capture
Internal conversion
Isomeric transition
 particle decay
A
Z
•
X
A 4
Z 2
Y  24 He  Q
Z>82   decay (most frequently)
Negatron particle decay
1
0
A
Z
n
1
1p
X
A
Z+1
+
0
-1 
+ u (anti-neutrino)
Y + 0-1  + u + Q
Positron particle decay
1
1
A
Z
p
1
0n
X
A
Z-1
0
++1 
Y +
+u
0
+1
(neutrino)
+u+Q
Electron Capture
1
1
0
-1
p+ e
A
Z
0
+ -1 e
X
1
0
n +u
A
Z-1
(neutrino)
Y +u+Q
Internal conversion
The excess nuclear energy is passed on to one of
the orbit electrons which is than ejected from the
atom.
Also induced:
-characteristic X-ray
-Auger electron
Isomeric transition
Tc  Tc  g
99 m
•
99
nuclei which are in excited states and which have a reasonably long lifetime are called
isomers. Transitions for which the change in angular momentum between the excited and
ground states is are designated isomeric transitions.
•
An excited nucleus may give off its excess an undergo a transition to the ground level with
the emission of an EM quantum i.e a X ray
γray