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General Physics (PHY 2140)
Lecture 35
¾ Modern Physics
9Atomic Physics
9The periodic table
9Atomic transitions
http://www.physics.wayne.edu/~apetrov/PHY2140/
Chapter 28
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Lightning Review
Last lecture:
1. Atomic physics
9 De Broglie waves/hydrogen atom
9 Quantum mechanics and spin
2π r = nλ , n = 1, 2,3,...
me vr = n=, n = 1, 2,3,...
 1 1 
= RH  2 − 2 
 n f ni 
λ


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Review Problem: An emission spectrum for hydrogen can be obtained by
analyzing the light from hydrogen gas that has been heated to very high
temperatures (the heating populates many of the excited states of hydrogen). An
absorption spectrum can be obtained by passing light from a broadband
incandescent source through hydrogen gas. If the absorption spectrum is obtained at
room temperature, when all atoms are in the ground state, the absorption spectrum
will
1. be identical to the emission spectrum.
2. contain some, but not all, of the lines appearing in the emission spectrum.
3. contain all the lines seen in the emission spectrum, plus additional lines.
4. look nothing like the emission spectrum.
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Quantum Number Summary
The values of n can increase from 1 in integer steps
The values of ℓ can range from 0 to n-1 in integer steps
The values of m ℓ can range from -ℓ to ℓ in integer steps
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28.9 The Pauli Exclusion Principle
Recall Bohr’s model of an atom. Why don’t all the
electrons stay on the lowest possible orbit?
Pauli’s exclusion principle: no two electrons in an atom
can ever be in the same quantum state
„
In other words, no two electrons in the same atom can have
exactly the same values for n, ℓ, m ℓ, and ms
This explains the electronic structure of complex atoms
as a succession of filled energy levels with different
quantum numbers
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Examples
1. Hydrogen (one electron), 1s1
n = 1, A = 0, mA = 0, ms = ±1
2. Helium (two electrons), 1s2
n = 1, A = 0, mA = 0, ms = + 1 2
n = 1, A = 0, mA = 0, ms = −1 2
3. Lithium (three electrons), 1s22s1
n = 1, A = 0, mA = 0, ms = + 1 2
n = 1, A = 0, mA = 0, ms = −1 2
n = 2, A = 0, mA = 0, ms = ± 1 2
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The Periodic Table
The outermost electrons are
primarily responsible for the
chemical properties of the
atom
Mendeleev arranged the
elements according to their
atomic masses and chemical
similarities
The electronic configuration
of the elements explained by
quantum numbers and Pauli’s
Exclusion Principle explains
the configuration
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Bit of history: Mendeleev’s original table
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Problem: electron configuration of O
(a) Write out the electronic configuration of the ground state
for oxygen (Z = 8). (b) Write out values for the set of
quantum numbers n, l, ml, and ms for each of the
electrons in oxygen.
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(a) Write out the electronic configuration of the ground state for oxygen (Z = 8). (b)
Write out values for the set of quantum numbers n, l, ml, and ms for each of the
electrons in oxygen.
Given:
Z=8
Recall that the number of electrons is the same as the
charge of the nucleus. Thus, we have 8 electrons.
n = 1, A = 0, mA = 0, ms = ± 1 2
n = 2, A = 0, mA = 0, ms = ± 1 2
n = 2, A = 1, mA = (0, 1), ms = ± 1 2
Find:
Thus, electron configuration is
1s 2 2s 2 2 p 4
structure
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QUICK QUIZ
Krypton (atomic number 36) has how many electrons in its next
to outer shell (n = 3)?
(a) 2
(c) 8
(b) 4
(d) 18
(d). Krypton has a closed configuration consisting of filled n=1, n=2,
and n=3 shells as well as filled 4s and 4p subshells. The filled n=3
shell (the next to outer shell in Krypton) has a total of 18 electrons, 2
in the 3s subshell, 6 in the 3p subshell and 10 in the 3d subshell.
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Characteristic X-Rays
When a metal target is
bombarded by high-energy
electrons, x-rays are emitted
The x-ray spectrum typically
consists of a broad continuous
spectrum and a series of sharp
lines
„ The lines are dependent on
the metal
„ The lines are called
characteristic x-rays
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Explanation of Characteristic X-Rays
The details of atomic structure can be used to explain
characteristic x-rays
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A bombarding electron collides with an electron in the target
metal that is in an inner shell
If there is sufficient energy, the electron is removed from the
target atom
The vacancy created by the lost electron is filled by an electron
falling to the vacancy from a higher energy level
The transition is accompanied by the emission of a photon
whose energy is equal to the difference between the two levels
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Moseley Plot
λ is the wavelength of the Kα
line
„ Kα is the line that is
produced by an electron
falling from the L shell to
the K shell
From this plot, Moseley was
able to determine the Z values
of other elements and produce
a periodic chart in excellent
agreement with the known
chemical properties of the
elements
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Atomic Transitions – Energy Levels
An atom may have many
possible energy levels
At ordinary temperatures, most
of the atoms in a sample are in
the ground state
Only photons with energies
corresponding to differences
between energy levels can be
absorbed
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Atomic Transitions – Stimulated Absorption
The blue dots represent
electrons
When a photon with energy
∆E is absorbed, one electron
jumps to a higher energy
level
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These higher levels are
called excited states
∆E = hƒ = E2 – E1
In general, ∆E can be the
difference between any two
energy levels
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Atomic Transitions – Spontaneous Emission
Once an atom is in an excited
state, there is a constant
probability that it will jump back
to a lower state by emitting a
photon
This process is called
spontaneous emission
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Atomic Transitions – Stimulated Emission
An atom is in an excited stated
and a photon is incident on it
The incoming photon
increases the probability that
the excited atom will return to
the ground state
There are two emitted
photons, the incident one and
the emitted one
„ The emitted photon is in
exactly in phase with the
incident photon
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Population Inversion
When light is incident on a system of atoms, both stimulated
absorption and stimulated emission are equally probable
Generally, a net absorption occurs since most atoms are in the
ground state
If you can cause more atoms to be in excited states, a net emission
of photons can result
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This situation is called a population inversion
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Lasers
To achieve laser action, three conditions must be met
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The system must be in a state of population inversion
The excited state of the system must be a metastable state
Its lifetime must be long compared to the normal lifetime of
an excited state
The emitted photons must be confined in the system long
enough to allow them to stimulate further emission from other
excited atoms
This is achieved by using reflecting mirrors
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Production of a Laser Beam
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Laser Beam – He Ne Example
The energy level diagram for Ne
The mixture of helium and neon is
confined to a glass tube sealed at
the ends by mirrors
A high voltage applied causes
electrons to sweep through the
tube, producing excited states
When the electron falls to E2 in
Ne, a 632.8 nm photon is emitted
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