NJIT Physics 320: Astronomy and Astrophysics – Lecture V Carsten Denker Physics Department Center...
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Transcript of NJIT Physics 320: Astronomy and Astrophysics – Lecture V Carsten Denker Physics Department Center...
NJIT
Physics 320: Astronomy and Astrophysics – Lecture V
Carsten Denker
Physics DepartmentCenter for Solar–Terrestrial Research
October 1st, 2003NJIT Center for Solar-Terrestrial Research
The Interaction of Light and MatterThe Interaction of Light and Matter
Spectral LinesSpectral LinesPhotonsPhotonsThe Bohr Model of the AtomThe Bohr Model of the AtomQuantum Mechanics and Wave–Quantum Mechanics and Wave–
Particle DualityParticle Duality
October 1st, 2003NJIT Center for Solar-Terrestrial Research
Electromagnetic Spectrum
October 1st, 2003NJIT Center for Solar-Terrestrial Research
Spectral Lines
Auguste Comte 1835 in Positive Philosophy: We see how we may determine their forms their distances, their bulk, their motions, but we can never know anything of their chemical or minerological structure.
William Wollaston, Joseph Fraunhofer, Robert Bunsen, Gustav Kirchhoff, … spectroscopy
October 1st, 2003NJIT Center for Solar-Terrestrial Research
Kirchhoff’s Laws
A hot (< 0 K), dense gas or solid object produces produces a continuous spectrum with no dark spectral lines.
A hot, diffuse gas produces bright spectral lines (emission lines).
A cool, diffuse gas in front of a source of a continuous spectrum produces dark spectral lines (absorption lines) in the continuous spectrum.
October 1st, 2003NJIT Center for Solar-Terrestrial Research
Spectroscopy
Prisms Diffraction gratings
Transmission grating Reflection grating
sin and 1, 2, 3, ...d n n
nN
nN
Resolving power
October 1st, 2003NJIT Center for Solar-Terrestrial Research
Photoelectric Effect
photon
hcE h
max photon
hcK E h
October 1st, 2003NJIT Center for Solar-Terrestrial Research
Compton Effect
photon
hcE h pc
1 cosf ie
h
m c
In a collision between a photon and an electron initially at rest, both the (relativistic) momentum and energy are conserved.
0.0243 Åce
h
m c
Compton wavelength
October 1st, 2003NJIT Center for Solar-Terrestrial Research
The Bohr Model of the Atom
Wave–particle duality of lightRutherford 1911 Au: It was quite
the most incredible event that ever happened to me in my life. It was almost as incredible as if you fired a 15–inch shell at a piece of tissue paper and it came back an hit you. discovery of a minute, massive, positively charged atomic nucleus
Proton: mp = 1836 me
October 1st, 2003NJIT Center for Solar-Terrestrial Research
Group AssignmentProblem 5.7
Verify that the units of Planck’s constant are the units of angular momentum!
2
2
-1 2
m m kg m = kg
s s
J m m = Js = Nm s = kg m s = kg
s s s
L mvr
EE h h
October 1st, 2003NJIT Center for Solar-Terrestrial Research
Hydrogen Atom1
2
1 1 1 and 109677.585 0.008 cm
4H HR Rn
2 2
1 1 1 and HR m n
m n
m = 1 UV [122, 103, 97, …] nm Lyman
m = 2 Visible [656, 486, 434, …] nm Balmer
m = 3 IR [1875, 1282, 1094, …] nm Paschen
m = 4 IR [4051, 2625, 2165, …] nm Brackett
m = 5 IR [7458, 4652, …] nm Pfundt
Planetary model of the hydrogen atom?
October 1st, 2003NJIT Center for Solar-Terrestrial Research
Bohr’s Postulates
Only orbits are stable, where the angular momentum of the electron is quantized L = nh/2=nħ, and will not radiate in spite of the electron’s acceleration.
Every allowed orbit corresponds to a distinct energy level and the transition from a distant orbit to an orbit closer to the nucleus Ephoton = Ehigh – Elow results in the emission of an energy quantum, i. e., a photon.
October 1st, 2003NJIT Center for Solar-Terrestrial Research
Bohr Atom1 2
30
1
4E
q qF r
r
Coloumb’s law
( )(1836 )0.9994556
1836e p e e
ee p e e
m m m mm
m m m m
Reduced mass
1836 1837e p e e eM m m m m m Total mass
and p eM m m
2 2 21 2
3 2 20 0
1 1
4 4
q q v e vF a r r
r r r r
October 1st, 2003NJIT Center for Solar-Terrestrial Research
2
0
12
8
eE K U K K K
r
2 22
0 0
1 1 1 and 2
2 8 4
e eK v U K
r r
h and =
2L vr n
Quantization of
angular momentum
2 222
2 20
1 1 1 1
8 2 2 2
vr neK v
r r r
22 2 11
0 0 024 and 5.29 10 m 0.529 Ånr n a n a
e
October 1st, 2003NJIT Center for Solar-Terrestrial Research
Bohr Atom (cont.)
2 4
2 2 20
1 1 113.6 eV
8 2nn
e eE
r n n
1 1 0
2 1 2 0
13.6 eV 0.529 Å
/ 4 3.40 eV 4 2.12 Å
E r a
E E r a
4 4
photon high low 2 2 2 2high low
1 1
2 2
hc e eE E E
n n
4 4
3 2 2 2 2 3high low high low
1 1 1 1 1 and
4 4H H
e eR R
c n n n n c
2 2
1 1( 13.6 eV) 1.89 eV 6565 Å
3 2HH
hcE
E
October 1st, 2003NJIT Center for Solar-Terrestrial Research
Kirchhoff’s Laws Revisited
A hot, dense gas or hot solid object produces a continuous spectrum with no dark spectral lines. This is the continuous spectrum of black body radiation, described by the Planck functions B(T) and B(T), emitted at any temperature above absolute zero. The wavelength max at which the Planck function B(T) obtains its maximum is given by Wien’s displacement law.
October 1st, 2003NJIT Center for Solar-Terrestrial Research
Kirchhoff’s Laws Revisited (cont.) A hot, diffuse gas produces bright emission lines. Emission lines
are produced when an electron makes a downward transition from a higher to a lower orbit. The energy lost by the electron is carried away by the photon.
A cool, diffuse gas in front of a source of continuous spectrum produces dark absorption lines in the continuous spectrum. Absorption lines are produced when an electron makes a transition from a lower to a higher orbit. If the incident photon in the continuous spectrum has exactly the right amount of energy, equal to the difference in energy between a higher orbit and the electron’s initial orbit, the photon is absorbed by the atom and the electron makes an upward transition to the higher orbit.
October 1st, 2003NJIT Center for Solar-Terrestrial Research
Quantum Mechanics and Wave–Particle Duality
E
h De Broglie frequency
h
p De Broglie
wavelength
1
2 or 1
2
x p x p
E tE t
Heisenberg’s uncertainty principle
October 1st, 2003NJIT Center for Solar-Terrestrial Research
Problem 4.5
2
moving2
moving
rest moving
moving rest
rest moving
10.8 1 0.6 and 60 m
( ) / 0.8 0.25 μs
60 m( ) 100 m
0.61
( ) 0.6 60 m 36 m
( ) 100 m/0.8c 0.417 μs
( ) 100 m 36 m 64 m
64 m / 0.8
P
T
T
u uL
c c
a t L c
b L L
c L L
d t
e L L
t c
0.267 μs
October 1st, 2003NJIT Center for Solar-Terrestrial Research
Problem 4.13
2
2
0.8 and 0.6 (Frame of reference @ rest = Earth)
(Eqn. 4.40)1 /
0.6 0.8= 0.946
1 (0.8 )( 0.6 ) /
0.946
A B
BB
B
A
v u c v c
v uv
uv c
c cc
c c c
v c
October 1st, 2003NJIT Center for Solar-Terrestrial Research
Problem 4.18
2
2 2 2
2 22 2 4 2 2 2 2 2 2
2 2 2 2 2
2 2
(Eqn. 4.46)
( )
(Eqn. 4.48) (1 ) (1 ) (1 )
if (1 ) 2
E mc
E mc
E m c mc mc mc mc mc mc
p c mc mc Kmc
p pK K v c
m m
October 1st, 2003NJIT Center for Solar-Terrestrial Research
Homework Class Project
Prepare a 200 – 250 word abstract for one of the five topics mentioned in the storyline
Important scientific factsForm of presentationLearning goalsHomework is due Wednesday
October 8th, 2003 at the beginning of the lecture!
Exhibition name competition!
October 1st, 2003NJIT Center for Solar-Terrestrial Research
Homework
Homework is due Wednesday October 8th, 2003 at the beginning of the lecture!
Homework assignment: Problems 5.4, 5.5, and 5.15
Late homework receives only half the credit!
The homework is group homework!Homework should be handed in as a
text document!