thurs. nov. 19, 2009phy208 lect. 23 1 exam 3 is thursday dec. 3 (after thanksgiving) students w /...
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Thurs. Nov. 19, 2009 Phy208 Lect. 23 1
Exam 3 is Thursday Dec. 3 (after Thanksgiving)
Students w / scheduled academic conflict please stay after class Tues. Nov. 24 to arrange alternate time.
5:30-7 pm, Birge 145
Covers: all material since exam 2.
Bring: Calculator
One (double-sided) 8 1/2 x 11 note sheet
Schedule:
Week14HW: assigned Thur. Nov. 19, due Fri. Dec. 4 (two weeks)
Last material for exam: Lecture of Tues. Nov. 24
Exam review: Tuesday, Dec. 1, in class
Thurs. Nov. 19, 2009 Phy208 Lect. 23 2
Summary of Photoelectric effect
Light comes in photons - particles of light h=Planck’s constant
Red photon is low frequency, low energy.
(Ultra)violet is high frequency, high energy.
Electron in metal absorbs one photon Can escape metal if photon energy large enough
Ephoton>Work function Eo
Excess energy Ephoton-Eo shows up as kinetic energy
€
E photon = hf = hc /λ
Thurs. Nov. 19, 2009 Phy208 Lect. 23 3
Photon properties of light Photon of frequency f has energy hf
Red light made of ONLY red photons The intensity of the beam can be increased by
increasing the number of photons/second. Photons/second = energy/second = power
€
E photon = hf = hc /λ
€
h = 6.626 ×10−34 J ⋅s = 4.14 ×10−15eV ⋅s
€
hc =1240eV ⋅nm
Thurs. Nov. 19, 2009 Phy208 Lect. 23 4
Quantization of light
Possible energies for green light (=500 nm)
E=hf
E=2hf
E=3hf
E=4hf
One quantum of energy:one photon
Two quanta of energytwo photons
etc
Think about light as a particle rather than wave.
Quantum mechanically, brightness can only be changed in steps, with energy differences of hf.
En
erg
y
Thurs. Nov. 19, 2009 Phy208 Lect. 23 5
Thompson’s model of atom
J.J. Thomson’s model of 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
This model is not correct!
Thurs. Nov. 19, 2009 Phy208 Lect. 23 6
Thurs. Nov. 19, 2009 Phy208 Lect. 23 7
Resulted in new model 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
Thurs. Nov. 19, 2009 Phy208 Lect. 23 8
Difference between atoms Simplest is Hydrogen:
1 electron orbiting 1 proton
Other atoms number of orbiting negative electrons same as number of
positive protons in nucleus Different elements have different number of
orbiting electrons Helium: 2 electrons Copper: 29 electrons Uranium: 92 electrons! Organized into periodic table of elements
First concentrate on hydrogen atom
Thurs. Nov. 19, 2009 Phy208 Lect. 23 9
Circular motion of orbiting electrons: electrons emit EM radiation at orbital frequency.
Similar to radio waves emitted by accelerating electrons in a antenna.
In an atom, emitted EM wave carries away energy Electron predicted to continually lose energy. The electron would eventually spiral into the nucleus However most atoms are stable!
Planetary model and radiation
Thurs. Nov. 19, 2009 Phy208 Lect. 23 10
Line spectra from atoms Atoms do emit radiation,
but only at certain discrete frequencies.
Emission pattern unique to different atoms
Spectrum is an atomic ‘fingerprint’, used to identify atoms (e.g. in space).
Hydrogen
Mercury
Wavelength (nm)
Thurs. Nov. 19, 2009 Phy208 Lect. 23 11
The Bohr atom Retained ‘planetary’ picture with
circular orbits
Only certain orbits are stable
Radiation emitted only when electron jumps from one stable orbit to another.
Here, the emitted photon has an energy ofEinitial-Efinal
Stable orbit
Stable orbit
Einitial
Efinal
Photon
Thurs. Nov. 19, 2009 Phy208 Lect. 23 12
Energy levels Instead of drawing orbits, just indicate energy an
electron would have if it were in that orbit.Zero energy
n=1
n=2
n=3
n=4
€
E1 = −13.6
12 eV
€
E2 = −13.6
22 eV
€
E3 = −13.6
32 eV
En
erg
y
axis
Thurs. Nov. 19, 2009 Phy208 Lect. 23 13
Hydrogen atom energiesZero energy
n=1
n=2
n=3
n=4
€
E1 = −13.6
12 eV
€
E2 = −13.6
22 eV
€
E3 = −13.6
32 eV
En
erg
y
€
En = −13.6
n2 eV
Quantized energy levels: Each corresponds to
different Orbit radius Velocity Particle wavefunction Energy
Each described by a quantum number n
Thurs. Nov. 19, 2009 Phy208 Lect. 23 14
Emitting and absorbing light
Photon is emitted when electron drops from one quantum state to another
Zero energy
n=1
n=2
n=3
n=4
€
E1 = −13.6
12 eV
€
E2 = −13.6
22 eV
€
E3 = −13.6
32 eV
n=1
n=2
n=3
n=4
€
E1 = −13.6
12 eV
€
E2 = −13.6
22 eV
€
E3 = −13.6
32 eV
Absorbing a photon of correct energy makes electron jump to higher quantum state.
Photon absorbed hf=E2-E1
Photon emittedhf=E2-E1
Thurs. Nov. 19, 2009 Phy208 Lect. 23 15
Hydrogen emission
This says hydrogen emits only photons of a particular wavelength, frequency
Photon energy = hf, so this means a particular energy.
Conservation of energy: Energy carried away by photon is lost by the orbiting
electron.
Thurs. Nov. 19, 2009 Phy208 Lect. 23 16
Hydrogen atomAn electron drops from an -1.5 eV energy level to one with
energy of -3.4 eV. What is the wavelength of the photon emitted?
A. 827 nmB. 653 nmC. 476 nmD. 365 nmE. 243 nm
Zero energy
n=1
n=2
n=3
n=4
€
E1 = −13.6 eV
€
E2 = −3.4 eV€
E3 = −1.5 eV
Photon emittedhf=E2-E1
hf = hc/ = 1240 eV-nm/
Thurs. Nov. 19, 2009 Phy208 Lect. 23 17
Each orbit has a specific energy En=-13.6/n2
Photon emitted when electron jumps from high energy to low energy orbit.
Ei – Ef = h f Photon absorption induces
electron jump from low to high energy orbit.
Ef – Ei = h f Agrees with experiment
Energy conservation for Bohr atom
Thurs. Nov. 19, 2009 Phy208 Lect. 23 18
Hydrogen emission spectrum Hydrogen is simplest atom
One electron orbiting around one proton.
The Balmer Series of emission lines empirically given by
€
1
λm= RH
1
22−
1
n2
⎛
⎝ ⎜
⎞
⎠ ⎟
n = 3, = 656.3 nm
Hydrogen
n = 4, = 486.1 nm
n=3n=4
Thurs. Nov. 19, 2009 Phy208 Lect. 23 19
Balmer series
Transitions terminate at n=2
Each energy level has energy
En=-13.6 / n2 eV
E.g. n to 2 transition Emitted photon has energy
Emitted wavelength
€
E photon = −13.6eV
n2
⎛
⎝ ⎜
⎞
⎠ ⎟− −
13.6eV
22
⎛
⎝ ⎜
⎞
⎠ ⎟
⎛
⎝ ⎜
⎞
⎠ ⎟=13.6 eV
1
22−
1
n2
⎛
⎝ ⎜
⎞
⎠ ⎟
€
λ =hc
E photon=
1240 eV − nm
13.6 eV
1
22−
1
n2
⎛
⎝ ⎜
⎞
⎠ ⎟−1
=91.18nm
1/22 −1/n2( )
Thurs. Nov. 19, 2009 Phy208 Lect. 23 20
Why stable orbits?Bohr argued that the stable orbits
are those for which the electron’s orbital angular momentum L is quantized as
€
L = me v r= n h
€
h=h
2π
⎛
⎝ ⎜
⎞
⎠ ⎟
Electron velocity
Electron orbit radius
Integer:n=1,2,3…
Bohr combined this with the Coulomb force to find allowed orbital radii and energies.
Thurs. Nov. 19, 2009 Phy208 Lect. 23 21
Including more physics
Circular orbit, electron is accelerating (centripetal acceleration = v2/r = Force/mass)
Force causing this accel. is Coulomb force ke2/r2
between pos. nucleus and neg. electron
Also gives a condition for angular momentum.
€
v 2
r =
FCoulombm
Thurs. Nov. 19, 2009 Phy208 Lect. 23 22
Bohr model of H-atom
Quantization:
Orbital motion:
€
v 2
r = FCoulomb /m = k
e2
r2/m
centripetal acceleration
Coulomb force / mass
€
L2 = mvr( )2
= n2h2€
L2 = mvr( )2
= mke2r€
p = mv
Thurs. Nov. 19, 2009 Phy208 Lect. 23 23
Radius of H-atom states
€
L2 = n2h2
€
L2 = mke2rand
Quantization Orbital motion
€
n2h2 = mke2r
r = n2 h2
mke2
⎛
⎝ ⎜
⎞
⎠ ⎟= n2ao
€
ao = Bohr radius
≈ 0.529ÅQuantized orbital radius
n orbit radius
1 ao
2 4ao
3 9ao
Thurs. Nov. 19, 2009 Phy208 Lect. 23 24
Energy of H-atom states
Total Energy = kinetic + potential
€
p2
2m
⎛
⎝ ⎜
⎞
⎠ ⎟ + −k
e2
r
⎛
⎝ ⎜
⎞
⎠ ⎟
ke2
2r
⎛
⎝ ⎜
⎞
⎠ ⎟ + −k
e2
r
⎛
⎝ ⎜
⎞
⎠ ⎟ = − k
e2
2r= −
ke2
2ao
⎛
⎝ ⎜
⎞
⎠ ⎟1
n2
€
En = −13.6 eV
n2Quantized energy
€
rn = n2ao
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