现代物理学PPT教学课件
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– Large scattering angles of alpha particles from atoms in a metal foil indicate a “hard” nuclear model.
Phys 320 - Baski
Topic 1: Nuclear Atomic Model
Page 2
– Bohr model predicts energy transitions for one-electron atoms.
• X-ray Spectra
– Analogous to optical spectra, but for higher-energy x-ray transitions of heavier, multi-electron elements.
rn
ao
n2 Z
where ao 0.0529 nm (Bohr radius)
En
Eo
Z2 n2
where Eo 13.6 eV (H ionization energy)
• Derivation uses the following:
1
rn
n mv
(Quantized
Ln )
v
• Franck-Hertz Experiment
– Quantized inelastic scattering of electrons in Hg gas provide evidence for atomic energy levels.
• Rutherford Scattering Experiment
hf
hc
Ei
Ef
• Note: The product hc of Planck’s constant h and the speed of light c gives: hc = 1240 eV nm in “Modern Physics” units.
Phys 320 - Baski
Topic 1: Nuclear Atomic Model
Atomic Spectra
• In 1885, Balmer observed Hydrogen spectrum and saw colored lines. – Found empirical formula for discrete wavelengths of lines. – Formula generalized by Rydberg for all one-electron atoms.
Phys 320 - Baski
Topic 1: Nuclear Atomic Model
Page 1
Topic 1: Nuclear Atomic Model
• Optical (Atomic) Spectra
– Lower-energy optical absorption/emission lines from materials indicate quantized electron energy levels.
Bohr Model: Transition Energy Problem
Find the energy E , frequency f , and wavelength of the series limit (i.e., highest energy transition) for the Brackett spectral series (nf = 4) of Be3+.
Phys 320 - Baski
Prism separates wavelengths
Q: Where is Red vs. Blue line?
Topic 1: Nuclear Atomic Model
Page 3
Atomic Spectra: Modern Physics Lab
Neon Tube
3.29 1015
s 1
Phys 320 - Baski
Topic 1: Nuclear Atomic Model
Page 11
Bohr Model : Unknown Transition Problem
If the energy of a particular transition in the Helium Paschen series is 2.644 eV, find the corresponding transition, i.e. initial and final n values.
12 121.6 nm Ultraviolet
Phys 320 - Baski
Topic 1: Nuclear Atomic Model
Page 6
Bohr Model
• Problem: Classical model of the electron “orbiting” nucleus is unstable. Why unstable? – Electron experiences centripetal acceleration. – Accelerated electron emits radiation. – Radiation leads to energy loss. – Electron eventually “crashes” into nucleus.
where h 6.58 1016 ev s
2
h = Planck's Constant
– Postulate #2: Atom radiates with quantized frequency f (or energy E) when electron makes a transition between two energy states.
Atomic Spectra: Hydrogen Energy Levels
E = 0 eV
Energy
n=3 n=2
Paschen Series (IR)
Balmer Series
(visible)
En
1 n2
Lyman Series (ultraviolet)
E1 = -13.6 eV
n=1
Lyman
Page 8
Bohr Model: Quantization of r, E
• Quantized angular momentum L leads to quantized radii and energies for an electron in a hydrogen atom or any ionized, one-electron atom.
Phys 320 - Baski
Topic 1: Nuclear Atomic Model
Page 12
Bohr Model: Ionization Energy Problem
Suppose that a He atom (Z=2) in its ground state (n = 1) absorbs a photon whose wavelength is = 41.3 nm. Will the electron be ionized?
1
Z2
Eo hc
1 n2f
1 ni2
or
hc
Ef
Ei
Z
2
Eo
1 n2f
1 ni2
• where hc = 1240 eV nm in “Modern Physics” units.
Phys 320 - Baski
Topic 1: Nuclear Atomic Model
Page 10
Ef
Ei
hc
Z
2
E0
1 nf 2
1 ni 2
where n f 4 for Brackett, ni = for Series Limit, Z 4 for Be
E
42
13.6
eV
1 42
1 2
13.6
eV
hc 1240 eV nm 91.2 nm E 13.6 eV
f
c
3108 m / s 91.2 109 m
E E f
Ei
Z
2 E0
1 nf 2
1 ni 2
1 ni 2
1 nf 2
E Z 2 E0
1/ 2
ni
1 nf 2
E Z 2 E0
where n f = 3 for Paschen Series, Z 2 for He
1/ 2
1 2.644 eV
ni 32 22 13.6 eV 4
• Solution: In 1913, Bohr proposed quantized model of the H atom to predict the observed spectrum.
Phys 320 - Baski
Topic 1: Nuclear Atomic Model
Page 7
Bohr Model: Quantization of L, f
Balmer Paschen
Example Data
Phys 320 - Baski
Topic 1: Nuclear Atomic Model
Page 5
Atomic Spectra: Rydberg Formula for H
For Hydrogen:
1
1
1
n f ni
R
n2 final
n2 initial
What is Modern Physics?
• Modern physics only came of age in the 1900’s. – Physicists discovered that Newtonian mechanics did not apply when objects were very small or moved very fast!
Eyepiece
(to observe lines)
High Voltage Supply
(to “excite” atoms)
Diffraction Grating
(to separate light)
Phys 320 - Baski
Topic 1: Nuclear Atomic Model
Page 4
• Plan for Physics 320. – Test #1: Nuclear Atom, Wave/Particle Duality, Wave Packets – Test #2: Schroedinger Equation, Atomic & Solid-state Physics – Nuclear Physics, Relativity
with
ni n f
• Rydberg constant R ~ 1.097 × 107 m-1 • nfinal = 1 (Lyman), 2 (Balmer), 3 (Paschen)
• Example for n = 2 to 1 transition:
ຫໍສະໝຸດ Baidu
1
12
1 12
1 22
R
3 (1.097 107 m1 ) 4
• If things are confined to very small dimensions (nanometer-scale), then QUANTUM mechanics is necessary. – Atomic orbitals, quantum heterostructures.
• Bohr proposed two “quantum” postulates:
– Postulate #1: Electrons exist in stationary orbits (no radiation) with quantized angular momentum.
Ln mvr n
kZe2 mr
2
(from centripetal and electric forces)
Phys 320 - Baski
Topic 1: Nuclear Atomic Model
Page 9
Bohr Model: IMPORTANT Energy Formula
• Energy transitions yield general Rutherford formula. – Applicable to ionized atoms of nuclear charge Z with only one electron.
• If things move very fast (close to the speed of light), then RELATIVISTIC mechanics is necessary. – Cosmic particles, atomic clocks (GPS), synchrotrons.
Phys 320 - Baski
Topic 1: Nuclear Atomic Model
Page 2
– Bohr model predicts energy transitions for one-electron atoms.
• X-ray Spectra
– Analogous to optical spectra, but for higher-energy x-ray transitions of heavier, multi-electron elements.
rn
ao
n2 Z
where ao 0.0529 nm (Bohr radius)
En
Eo
Z2 n2
where Eo 13.6 eV (H ionization energy)
• Derivation uses the following:
1
rn
n mv
(Quantized
Ln )
v
• Franck-Hertz Experiment
– Quantized inelastic scattering of electrons in Hg gas provide evidence for atomic energy levels.
• Rutherford Scattering Experiment
hf
hc
Ei
Ef
• Note: The product hc of Planck’s constant h and the speed of light c gives: hc = 1240 eV nm in “Modern Physics” units.
Phys 320 - Baski
Topic 1: Nuclear Atomic Model
Atomic Spectra
• In 1885, Balmer observed Hydrogen spectrum and saw colored lines. – Found empirical formula for discrete wavelengths of lines. – Formula generalized by Rydberg for all one-electron atoms.
Phys 320 - Baski
Topic 1: Nuclear Atomic Model
Page 1
Topic 1: Nuclear Atomic Model
• Optical (Atomic) Spectra
– Lower-energy optical absorption/emission lines from materials indicate quantized electron energy levels.
Bohr Model: Transition Energy Problem
Find the energy E , frequency f , and wavelength of the series limit (i.e., highest energy transition) for the Brackett spectral series (nf = 4) of Be3+.
Phys 320 - Baski
Prism separates wavelengths
Q: Where is Red vs. Blue line?
Topic 1: Nuclear Atomic Model
Page 3
Atomic Spectra: Modern Physics Lab
Neon Tube
3.29 1015
s 1
Phys 320 - Baski
Topic 1: Nuclear Atomic Model
Page 11
Bohr Model : Unknown Transition Problem
If the energy of a particular transition in the Helium Paschen series is 2.644 eV, find the corresponding transition, i.e. initial and final n values.
12 121.6 nm Ultraviolet
Phys 320 - Baski
Topic 1: Nuclear Atomic Model
Page 6
Bohr Model
• Problem: Classical model of the electron “orbiting” nucleus is unstable. Why unstable? – Electron experiences centripetal acceleration. – Accelerated electron emits radiation. – Radiation leads to energy loss. – Electron eventually “crashes” into nucleus.
where h 6.58 1016 ev s
2
h = Planck's Constant
– Postulate #2: Atom radiates with quantized frequency f (or energy E) when electron makes a transition between two energy states.
Atomic Spectra: Hydrogen Energy Levels
E = 0 eV
Energy
n=3 n=2
Paschen Series (IR)
Balmer Series
(visible)
En
1 n2
Lyman Series (ultraviolet)
E1 = -13.6 eV
n=1
Lyman
Page 8
Bohr Model: Quantization of r, E
• Quantized angular momentum L leads to quantized radii and energies for an electron in a hydrogen atom or any ionized, one-electron atom.
Phys 320 - Baski
Topic 1: Nuclear Atomic Model
Page 12
Bohr Model: Ionization Energy Problem
Suppose that a He atom (Z=2) in its ground state (n = 1) absorbs a photon whose wavelength is = 41.3 nm. Will the electron be ionized?
1
Z2
Eo hc
1 n2f
1 ni2
or
hc
Ef
Ei
Z
2
Eo
1 n2f
1 ni2
• where hc = 1240 eV nm in “Modern Physics” units.
Phys 320 - Baski
Topic 1: Nuclear Atomic Model
Page 10
Ef
Ei
hc
Z
2
E0
1 nf 2
1 ni 2
where n f 4 for Brackett, ni = for Series Limit, Z 4 for Be
E
42
13.6
eV
1 42
1 2
13.6
eV
hc 1240 eV nm 91.2 nm E 13.6 eV
f
c
3108 m / s 91.2 109 m
E E f
Ei
Z
2 E0
1 nf 2
1 ni 2
1 ni 2
1 nf 2
E Z 2 E0
1/ 2
ni
1 nf 2
E Z 2 E0
where n f = 3 for Paschen Series, Z 2 for He
1/ 2
1 2.644 eV
ni 32 22 13.6 eV 4
• Solution: In 1913, Bohr proposed quantized model of the H atom to predict the observed spectrum.
Phys 320 - Baski
Topic 1: Nuclear Atomic Model
Page 7
Bohr Model: Quantization of L, f
Balmer Paschen
Example Data
Phys 320 - Baski
Topic 1: Nuclear Atomic Model
Page 5
Atomic Spectra: Rydberg Formula for H
For Hydrogen:
1
1
1
n f ni
R
n2 final
n2 initial
What is Modern Physics?
• Modern physics only came of age in the 1900’s. – Physicists discovered that Newtonian mechanics did not apply when objects were very small or moved very fast!
Eyepiece
(to observe lines)
High Voltage Supply
(to “excite” atoms)
Diffraction Grating
(to separate light)
Phys 320 - Baski
Topic 1: Nuclear Atomic Model
Page 4
• Plan for Physics 320. – Test #1: Nuclear Atom, Wave/Particle Duality, Wave Packets – Test #2: Schroedinger Equation, Atomic & Solid-state Physics – Nuclear Physics, Relativity
with
ni n f
• Rydberg constant R ~ 1.097 × 107 m-1 • nfinal = 1 (Lyman), 2 (Balmer), 3 (Paschen)
• Example for n = 2 to 1 transition:
ຫໍສະໝຸດ Baidu
1
12
1 12
1 22
R
3 (1.097 107 m1 ) 4
• If things are confined to very small dimensions (nanometer-scale), then QUANTUM mechanics is necessary. – Atomic orbitals, quantum heterostructures.
• Bohr proposed two “quantum” postulates:
– Postulate #1: Electrons exist in stationary orbits (no radiation) with quantized angular momentum.
Ln mvr n
kZe2 mr
2
(from centripetal and electric forces)
Phys 320 - Baski
Topic 1: Nuclear Atomic Model
Page 9
Bohr Model: IMPORTANT Energy Formula
• Energy transitions yield general Rutherford formula. – Applicable to ionized atoms of nuclear charge Z with only one electron.
• If things move very fast (close to the speed of light), then RELATIVISTIC mechanics is necessary. – Cosmic particles, atomic clocks (GPS), synchrotrons.