Download Document

General Physics (PHY 2140)
Lecture 17
 Modern Physics
Atomic Physics
Electron Clouds
The Pauli Exclusion Principle
Characteristic X-Rays
Atomic Transitions
Lasers and Holography
Chapter 28
5/24/2017
http://www.physics.wayne.edu/~alan/2140Website/Main.htm
1
Lightning Review
Last lecture:
1. Quantum physics
 Atomic Descriptions
 Atomic Spectra
 Bohr’s Atomic Theory
 Quantum Mechanics
 Quantum Numbers
2 r  n , n  1, 2,3,...
Ei  E f  hf
mevr  n , n  1, 2,3,...
 1
1 
 RH  2  2 
 n f ni 



1
Review Problem: Suppose that the electron in the hydrogen atom obeyed
classical rather then quantum mechanics. Why should such an atom emit a
continuous rather then discrete spectrum?
If hydrogen obeyed classical physics, we would have no quantized
electron orbits. Therefore the transitions between orbits (energy
levels) could be arbitrarily large or small. This leads to a continuous
spectrum of emitted light.
5/24/2017
2
Electron Clouds
The graph shows the solution
to the wave equation for
hydrogen in the ground state

The curve peaks at the
Bohr radius

The electron is not
confined to a particular
orbital distance from the
nucleus
The probability of finding the
electron at the Bohr radius is a
maximum
5/24/2017
3
Electron Clouds
The wave function for
hydrogen in the ground state is
symmetric

The electron can be found
in a spherical region
surrounding the nucleus
The result is interpreted by
viewing the electron as a cloud
surrounding the nucleus

The densest regions of the
cloud represent the highest
probability for finding the
electron
5/24/2017
4
radial probability distribution (r 2 2) = probability of finding
electron at a distance r from the center of the nucleus
90% Probability contours showing relative size of orbitals
5/24/2017
5
5/24/2017
6
5/24/2017
7
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
5/24/2017
8
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
5/24/2017
9
Examples
1. Hydrogen (one electron), 1s1
n  1,  0, m  0, ms  1/ 2
2. Helium (two electrons), 1s2
n  1,  0, m  0, ms   1 2
n  1,  0, m  0, ms  1 2
3. Lithium (three electrons), 1s22s1 n  1,  0, m  0, ms   1 2
n  1,  0, m  0, ms  1 2
n  2,  0, m  0, ms   1 2
See Table 28.4 for other the configurations of other elements.
5/24/2017
10
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:
1s,2s,2p,3s,3p,4s,3d,4p,5s,4d
5/24/2017
11
Bit of history: Mendeleev’s original table
5/24/2017
12
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.
5/24/2017
13
(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,  0, m  0, ms   1 2
n  2,  0, m  0, ms   1 2
n  2,  1, m  (0, 1), ms   1 2
Find:
Thus, the electron configuration is:
1s 2 2s 2 2 p 4
structure
5/24/2017
14
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.
5/24/2017
15
= 2n2
+
5/24/2017
Recall: Kr needs 36 electrons, the remainder are in the N shell.
28
16
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
5/24/2017
17
Explanation of Characteristic X-Rays
The details of atomic structure can be used to explain
characteristic x-rays




5/24/2017
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
18
Modifications to Bohr’s Theory
For atoms with a larger nuclear charge, but with a single
electron (He+, Li2+, Be3+), we must modify the energy to
be:
me ke2 Z 2e4
Z 2 (13.6)
En  

(eV) n  1, 2, 3,
2 2
2
2 n
n
(Note the difference is the inclusion of Z, the number of protons in
the nucleus)
5/24/2017
19
Modifications to Bohr’s Theory, cont.
Since the energy of an emitted photon is the difference
between energy levels, we can write the wavelength of
such a photon as:
me ke2 Z 2 e4  1 1 

 2  2  n  1, 2, 3,
3

4 c
 n f ni 
1
Or as:
5/24/2017
me ke2e4  1 1 
Z
 2
3 
2

4 c  n f ni 
1
20
Moseley Plot
λ is the wavelength of the K
line

K is the line that is
produced by an electron
falling from the L shell
(n=2) to the K shell (n=1)
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
5/24/2017
21
Problem: X-Rays from Nickel
The K x-ray is emitted when an electron undergoes a
transition form the L shell (n=2) to the K shell (n=1) in a
metal. Calculate the wavelength of the K x-ray from a
nickel target, Z=28.
5/24/2017
22
The K x-ray is emitted when an electron undergoes a transition form the L shell (n=2)
to the K shell (n=1) in a metal. Calculate the wavelength of the K x-ray from a nickel
target, Z=28.
The atomic number for nickel is Z = 28. Using eq. 28.18 and
28.20 we have:
Given:
Z = 28
En  
Z eff2 (13.6)
n
2
eV
EK  (28  1) 2 (13.6 eV)  9.91103 eV
2 (13.6 eV)
3
EL  (28  3)


2.13

10
eV
2
(2)
hc
E  EL  EK  7.78 keV 

Find:

Thus, the wavelength is:
hc (6.63 1034 J s)(3.00 108 m/s)


E
7.78 keV(1.60 1016 J/keV)
 1.60 1010 m  0.160 nm
5/24/2017
23
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
5/24/2017
24
Atomic Transitions – Stimulated Absorption
The blue dots represent
electrons
When a photon with energy
ΔE is absorbed, one electron
jumps to a higher energy
level



5/24/2017
These higher levels are
called excited states
ΔE = hƒ = E2 – E1
In general, ΔE can be the
difference between any two
energy levels
25
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
5/24/2017
26
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
5/24/2017
27
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

5/24/2017
This situation is called a population inversion
28
Lasers
To achieve laser action, three conditions must be met



5/24/2017
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
29
Production of a Laser Beam
5/24/2017
30
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
(3s2  2p4)
5/24/2017
31
A More Detailed Diagram of a He-Ne Laser Operation
5/24/2017
32
Holography
Holography is the production of
three-dimensional images of an
object
Light from a laser is split at B
One beam reflects off the object
and onto a photographic plate
The other beam is diverged by
Lens 2 and reflected by the
mirrors before striking the film
5/24/2017
33
Holography, cont
The two beams form a complex interference pattern on the
photographic film


It can be produced only if the phase relationship of the two waves
remains constant
This is accomplished by using a laser
The hologram records the intensity of the light and the phase
difference between the reference beam and the scattered beam
The image formed has a three-dimensional perspective
5/24/2017
34