Transcript Document

General Physics (PHY 2140)
Lecture 32
 Modern Physics
Atomic Physics
Early models of the atom
Atomic spectra
http://www.physics.wayne.edu/~apetrov/PHY2140/
Chapter 28
7/20/2015
1
If you want to know your progress so far, please
send me an email request at
[email protected]
7/20/2015
2
Lightning Review
Last lecture:
1. Quantum physics
 Wave function
 Uncertainty relations
h
2
h
E t 
2
xp 
Review Problem:
Does the process of pair production (photon → e+ e- in the vicinity of a heavy
nucleus) violate conservation of mass?
(1) yes
(2) no
(3) what mass?
7/20/2015
3
Problem: Macroscopic measurement
A 0.50-kg block rests on the icy surface of a frozen pond, which we
can assume to be frictionless. If the location of the block is measured
to a precision of 0.50 cm, what speed must the block acquire because
of the measurement process?
7/20/2015
4
Atomic physics
7/20/2015
5
Importance of Hydrogen Atom
Hydrogen is the simplest atom
The quantum numbers used to characterize the allowed
states of hydrogen can also be used to describe
(approximately) the allowed states of more complex
atoms

This enables us to understand the periodic table
The hydrogen atom is an ideal system for performing
precise comparisons of theory and experiment

Also for improving our understanding of atomic structure
Much of what we know about the hydrogen atom can be
extended to other single-electron ions

7/20/2015
For example, He+ and Li2+
6
Early Models of the Atom
J.J. Thomson’s model of
the atom


A volume of positive charge
Electrons embedded
throughout the volume
A change from Newton’s
model of the atom as a
tiny, hard, indestructible
sphere
“watermelon” model
7/20/2015
7
Experimental tests
Expect:
1.
2.
Mostly small
angle scattering
No backward
scattering events
Results:
1.
2.
7/20/2015
Mostly small
scattering events
Several
backward
scatterings!!!
8
Early Models of the Atom
Rutherford’s model




7/20/2015
Planetary model
Based on results of thin foil
experiments
Positive charge is
concentrated in the center
of the atom, called the
nucleus
Electrons orbit the nucleus
like planets orbit the sun
9
Problem: Rutherford’s model
The “size” of the atom in Rutherford’s model is about 1.0 × 10–10 m.
(a) Determine the attractive electrical force between an electron
and a proton separated by this distance.
(b) Determine (in eV) the electrical potential energy of the atom.
7/20/2015
10
The “size” of the atom in Rutherford’s model is about 1.0 × 10–10 m. (a) Determine the
attractive electrical force between an electron and a proton separated by this
distance. (b) Determine (in eV) the electrical potential energy of the atom.
Electron and proton interact via the Coulomb force
Given:
r = 1.0 ×
10–10
m
F  ke
q1q2
r2



8.99 109 N  m2 C 2 1.60 1019 C
1.0 10
10
m


2
2
 2.3 108 N
Find:
(a) F = ?
(b) PE = ?
7/20/2015
Potential energy is
q1q2
1eV

18 
PE  ke
 2.3 10 J 
  14 eV
19
r
 1.6 10 J 
11
Difficulties with the Rutherford Model
Atoms emit certain discrete characteristic frequencies of
electromagnetic radiation

The Rutherford model is unable to explain this phenomena
Rutherford’s electrons are undergoing a centripetal
acceleration and so should radiate electromagnetic
waves of the same frequency


7/20/2015
The radius should steadily decrease as this radiation is given off
The electron should eventually spiral into the nucleus
It doesn’t
12
28.2 Emission Spectra
A gas at low pressure has a voltage applied to it
A gas emits light characteristic of the gas
When the emitted light is analyzed with a spectrometer, a series of
discrete bright lines is observed


Each line has a different wavelength and color
This series of lines is called an emission spectrum
7/20/2015
13
Emission Spectrum of Hydrogen
The wavelengths of hydrogen’s spectral lines can be found from
1
1
 1
 RH  2  2 

2 n 

RH is the Rydberg constant
RH = 1.0973732 x 107 m-1


n is an integer, n = 1, 2, 3, …
The spectral lines correspond to
different values of n
A.k.a. Balmer series
Examples of spectral lines


n = 3, λ = 656.3 nm
n = 4, λ = 486.1 nm
7/20/2015
14
Absorption Spectra
An element can also absorb light at specific wavelengths
An absorption spectrum can be obtained by passing a continuous
radiation spectrum through a vapor of the gas
The absorption spectrum consists of a series of dark lines
superimposed on the otherwise continuous spectrum

The dark lines of the absorption spectrum coincide with the bright lines
of the emission spectrum
7/20/2015
15
Applications of Absorption Spectrum
The continuous spectrum emitted by the Sun passes
through the cooler gases of the Sun’s atmosphere


7/20/2015
The various absorption lines can be used to identify elements in
the solar atmosphere
Led to the discovery of helium
16