Topic 3 - Review of Fundamentals
Atomic And Nuclear Structure
of Bohr’s Model
Rutherford’s Nuclear Atom
positive charge in center of atom, called NUCLEUS
tested by Geiger and Marsden
- Gold foil
Gold Foil Experiment
Bohr’s Atomic Model
model: solar system concept
classical theory predicted model unstable
1913, Neils Bohr – denied validity of classical electromagnetic theory
- New: (Max
Planck) quantum theory of radiation
adopted Planck’s theory
Bohr’s Model for Hydrogen
around nucleus in a circular orbit
in an orbit is proportional to its distance from the nucleus. The further
from the nucleus, the more energy it has
it stays in a stationary orbit, it does not emit radiation
a limited number of orbits with certain energies are allowed (quantization
of orbits using Planck's hypothesis)
have angular momentum as integral multiple of Planck's constant divided
only pass from one stationary state to another.
is absorbed when one jumps to a higher energy orbit
when an one falls into a lower energy orbit.
energy of the radiation emitted or absorbed is exactly equal to the difference
between the energies of the orbits
Bohr Atomic Model
Modification of the Bohr Atom
theory inadequate for even H atom
of spectral lines
are elliptical, not spherical, restricted by quantum conditions
atom by 4 quantum numbers
of several quantities that identify the state of a physical system
such as an atom, a nucleus, or a subatomic particle
- he principal
quantum number for atomic electrons indicates the energy state
and the probability of finding the electrons at various distances
from the nucleus
larger this number, the greater the energy is and the farther the electron
is likely to be from the nucleus
four quantum number are sufficient to uniquely characterize uniquely each
0 to n -1
-l to +l
-1/2, + 1/2
quantum numbers are needed to specify each orbital in an
most important is the principal quantum number, n (the same that Bohr introduced)
principal quantum number specifies the energy of the electron in the orbital
- As n increases
from its lowest value 1 through its allowed values 2, 3, . . . , the energies
of the corresponding orbitals increase.
Principle Quantum Number
- n labels the shell of the atom.
- has n2 individual
orbitals with the same principal quantum number
orbitals that lie at approximately the same distance from the nucleus.
the layers of an onion, with successive shells surrounding the inner shells.
Principal Quantum Number
- n = 1
electron in the orbital closest to the nucleus.
required to elevate the electron from n = 1 to n = ¥
required to remove the electron completely from the atom.
Azimuthal Quantum Number
angular momentum quantum
represents the magnitude of the orbital angular momentum of the electron
around the nucleus.
- as l increases,
the rate at which the electron circulates around the nucleus increases.
values of l in a shell of principal quantum number n are
limited to the n
values 0, 1, 2, . . . , n - 1
value of l in a given shell determines the subshell to which that orbital belongs.
- n subshells in a shell of principal
quantum number n.
- 2l +
1 orbitals in a given subshell.
labels for subshells:
- l = 0 is called an s subshell,
- l = 1 is called a p subshell,
- l = 2 is called a d subshell.
three subshells of the shell with n = 3 are called the 3s, 3p, and
Magnetic Quantum Number
- Subshell l consists
of 2 l + 1 individual orbitals.
- s subshell (l = 0) consists
of a single s orbital
- p subshell (l = 1) consists
of three p orbitals;
- d subshell (l = 2) consists
of five d orbitals
individual orbitals are labeled with the magnetic quantum number, ml, which
can take the 2 l + 1 values l, l - 1, . . . , -l.
(principal quantum number) defines electron shells. Values are integers (n = 1,2,3,4,...).
- l (azimuthal quantum number)defines atomic orbitals. Values are integers from 0
(magnetic quantum number) defines number of orbitals of a given kind. Values
are integers ranging from -l through 0 to +l.
(spin quantum number) has values of +½ and -½ (spin up, spin
Pauli Exclusion Principle: no two electrons can have the same set of four
s orbital example
The spherical boundary surface of an s orbital. This sphere
shows the region of space in which there is the highest probability of finding
an electron that is described by the corresponding wavefunction
The boundary surfaces of the three p orbitals of a given shell.
They are labeled according to their orientation relative to the three axes.
An electron described by one of these wavefunctions will not be found at
the nucleus; there is a nodal plane running through the nucleus between
the two lobes.
The boundary surfaces of the five d orbitals of a given shell,
Periodic Table of the Elements
with Bohr’s atomic model by application of Pauli exclusion principle
Periodic Table of the Elements
Periodic Table, again
complete electron shells constitute the core or kernel
energy of the kernel electrons is much higher than that of the valence
or conduction electrons.
electrons remain practically undisturbed in most of the processes in
which the atom participates.
Consequence of Periodicity
ejected from the kernel (e.g, K shell)
with n=1,2,3,4 constitute the K,L,M,M,.. shells
state (or hole) is left in K-shell
electron in a higher energy level can fall into the vacant state
emitted by electron "falling" into vacant state is in the X-ray
from: L,M,N,... valence shells
of X-ray lines may be produced designated as a, b etc.
Atomic Shell Terminology
Spectroscopists use n = 1, 2, 3, ..
spectroscopists use K, L, M, N, O . .
an electron is removed from a particular shell,
from all the higher-energy shells fill that vacancy
in a series that appears inverted as compared with the hydrogen series.
angular momentum states for a given shell cause energy sublevels within
- these subshells are labeled by Roman numerals according
to their energies.
Origin of Characteristic X-rays
Isotopes and Nuclides
- A is atomic mass number (protons + neutrons)
- Z is atomic number (protons)
- N is neutron number
- X is chemical symbol
energy released if a nuclide were synthesized from Z separate H atoms
and N (equal to A - Z) separate neutrons.
binding energy per nucleon shows a maximum at 56Fe falling
off gradually on both sides to about 7 MeV at 4He and to about
7.4 MeV for the most massive nuclei known.
of the naturally occurring nuclei are not stable in an absolute
= Zm(H) + (A-Z)m(N)
of sum of parts > actual weight
- mass defect
- d = W – M
mass equivalent of work done to separate nucleus into components,
- in energy
units, called Binding energy (BE)
(W – M)amu x 931 MeV/amu
- Eb =
Binding Energy per Nucleon
heavier than iron gain energy by degrading into products closer to iron
for heavy elements does alpha decay and spontaneous fission attain observable
energy is gained by fusion of most elements lighter than iron
repulsion keeps fusion rates low
if nuclei are subjected to greater than 107 K in hot cores
of stars, thermonuclear bombs, controlled fusion plasmas
- Building blocks known (n, p, subatomics)
- No definite structure defined
- Analogous to atomic system
- Three major models:
- Liquid drop
- Shell model
- Combined model
Liquid Drop Model
(1936) by Niels Bohr and used (1939) by him and John A. Wheeler to explain
(neutrons and protons) behave like the molecules in a drop of liquid.
given sufficient extra energy (as by the absorption of a neutron), the
spherical nucleus may be distorted into a dumbbell shape and then split
at the neck into two nearly equal fragments, releasing energy.
Liquid Drop Model– Bohr & Wheeler
inadequate to explain all nuclear phenomena, provides excellent estimates
of average properties of nuclei
homogenous mixture of nucleons
energy equally distributed
tension keeps nucleus spherical
calculation of atomic masses
binding energy can be understood with the model of a charged liquid drop.
Shell Nuclear Model
of nuclei similar to Bohr atomic model of electron energy levels.
by the American physicist Robert Hofstadter in the 1950s.
nuclear particles are paired
with neutron and proton with proton
numbers: filled nuclear-energy levels when the number of protons or neutrons
equals 2, 8, 20, 28, 50, 82, or 126indicate especially stable nuclei.
- The unpaired
neutrons and protons account for the properties of a particular species
of nucleus as valence electrons account for the chemical properties of the
- The shell
model accurately predicts certain properties of normal nuclei, such
as their angular momentum;
called UNIFIED MODEL, Incorporates
aspects of both the shell
the liquid-drop model Explains
certain magnetic and electric properties that neither of the two
separately can explain:
states of the nucleus
magnetic and electric properties (magnetic and quadrupole moments)
by the motion of the nucleons outside the closed shells
combined with the motion of the paired nucleons in the core.
of as a liquid drop on whose surface circulates a stable
tidal bulge directed toward the rotating unpaired nucleons outside
of protons (positively charged particles) constitutes a current
that in turn contributes to the magnetic properties of the nucleus,
greater deformation of the nucleus as the number of unpaired
nucleons increases accounts for the measured electric
quadrupole moment (an
index of nuclear shape - a measure of how much
the charge in space departs from spherical symmetry).
Nuclear Decay Schemes
- Binding energies
- Proton vs neutron number
- Table of isotopes
Chart of the Nuclides
Nuclear binding energies, shown as a function of atomic mass number
Nuclear Stability Curve