Office Hrs
• W 2:10-3:10 pm
• F after lecture
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tmontaruli@icecube.wisc.edu
http://www.icecube.wisc.edu/~tmontaruli
Chamberlin Hall - room 4112
Tel. +1-608-890-0901
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This week: more on atom
DC circuits
Magnetic Fields and Induction
EM waves
Cosmology
MTE3 25 April
1
What’s your view of atoms?
These 2-3 lectures concern:
Bohr atom, X-ray spectra, Frank&Hertz exp. (Ch 4 T&L)
Schroedinger equation for H atom, Periodic table and Pauli
exclusion principle (Ch 7 T&L)
2
All in Ch 36 of T&M
Hystory of Atoms
• Thompson’s classical model (1897)
• Problem: charges cannot be in equilibrium
Rutherford’s experiment (1911)
Planetary model
 Positive charge concentrated in the
nucleus (∼ 10-15 m)
 Electrons orbit the nucleus (r~10-10 m)
α particles
Thin gold foil
Problem1: emission and absorption at specific frequencies
Problem2: electrons on circular orbits radiate 3
Emission and Absorption spectra
Emission spectra: produced by gases where the atom do not experience many
collisions. Excited unbound atoms make transitions from excited states to lower levels
emitting photons
Absorption spectra: light crosses gas and atoms absorb at characteristic frequencies.
Re-emitted light has different frequencies hence dark lines
Continuum spectra: collisions broaden lines and individual lines are no more resolved
http://jersey.uoregon.edu/vlab/elements/Elements.html
4
Emitting and absorbing light
Zero energy
n=4
n=3
13.6
E 3 = − 2 eV
3
n=2
E2 = −
Photon
emitted
hf=E2-E1
€
13.6
eV
22
€
€
E3 = −
13.6
eV
32
n=2
E2 = −
13.6
eV
22
E1 = −
13.6
eV
12
Photon
absorbed
hf=E2-E1
13.6
E1 = − 2 eV
1
n=1
n=4
n=3
€
€
n=1
€
5
Hydrogen spectra
• Lyman Series of emission lines given by
n=2,3,4,..
Lyman series
R = 1.096776 x 107 /m
Use E=hc/λ
Rydberg-Ritz
Hydrogen
For heavy atoms R∞ = 1.097373 x 107 /m
6
Bohr’s Model of Hydrogen Atom (1913)
•Postulate 1: Electron moves in circular orbits where it does not radiate
(stationary states)
2
Orbit radius: rn = n a0
•Postulate 2: radiation emitted in transitions between stationary states
E i − E f = hν
•orbital angular momentum quantized
L = mvr = n h/2π
Zero
energy
€
n=4
n=3
E3 = −
13.6
eV
32
n=2
E2 = −
13.6
eV
22
€
Energy
axis
13.6
E n = − 2 eV
n
€
E1 = −
n=1
€
€
13.6
eV
12
7
Quantization in physics

“correspondence principle”


quantum mechanics must agree with classical results
when appropriate (large orbits and energies)
Incorporating wave nature of electron gives an
intuitive understanding of ‘quantized orbits’
8
Resonances of a string
λ/2
λn =
Fundamental,
...
wavelength 2L/1=2L,
frequency f
€
n=4
1st harmonic,
wavelength 2L/2=L,
frequency 2f
λ/2
2nd harmonic,
wavelength 2L/3,
frequency 3f
frequency
λ/2
2L
n
n=3
n=2
n=1
Vibrational modes equally
spaced in frequency
9
H atom question


Peter Flanary’s sculpture ‘Wave’ outside Chamberlin
What quantum state of H?

Integer number of wavelengths
around circumference.
L = pr = n
h
h
h
⇒ =n
⇒ 2πr = nλ
2π
λ
2πr
10
Radius and Energy levels of H-atom
2
 h2  n 2
r=n 
= a0
2
mkZe

 Z
2
2
Ze
v
=
m
r2
r
mvr = nh
F=k
€
€
2
2
2 2
4
2
p
kZe
1
k
Z
me
Z
Total energy: E =
−
⇒ E =−
= −13.6eV 2
2 2
2m
r
2 n h
n
This formula agrees to 6 significant digits. For better agreement we have to
m
consider the ‘reduced mass’: µ =
€
1+ m / M
pe = pN = p
2


p2
p2
1
m
+
M
p
EK =
+
= € p 2
=
2m 2mN 2  mM  2µ
€
11
X-ray spectra
• observed when bombarding target element with high energy electrons
in an X-ray tube
• When an electron is extracted from the inner shell and an outer electron
fills the leftover vacant state, photons are emitted at specific frequencies
• Moseley measured K α for many elements
L(n=2)->K(n=1)
€
M(n=3)->K(n=1)
12
X-ray spectra
ν = A(Z − b)
€

13.6eVZ 2  1
E 2 − E1 = hν ⇒ −
 2 −1
2
n

n
€
Franck and Hertz experiment (1914)
V0
4.9eV=E1-E0
6.7eV=E2-E0
electrons accelerated up to the energy
corresponding to the energy difference
between the n level and the fundamental
level lose energy in inelastic collisions
with Hg atoms or there can be multiple
inelastic collisions
14