现代物理学PPT教学课件

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.
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.
Atomic Spectra: Hydrogen Energy Levels
E = 0 eV
Energy
n=3 n=2
Paschen Series (IR)
Balmer Series
(visiblultraviolet)
E1 = -13.6 eV
n=1
Lyman
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!
• If things move very fast (close to the speed of light), then RELATIVISTIC mechanics is necessary. – Cosmic particles, atomic clocks (GPS), synchrotrons.
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
• 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
– 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.
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.
• Franck-Hertz Experiment
– Quantized inelastic scattering of electrons in Hg gas provide evidence for atomic energy levels.
• Rutherford Scattering Experiment
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
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
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
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
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.
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?
• If things are confined to very small dimensions (nanometer-scale), then QUANTUM mechanics is necessary. – Atomic orbitals, quantum heterostructures.
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
– 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
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
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+.
• Bohr proposed two “quantum” postulates:
– Postulate #1: Electrons exist in stationary orbits (no radiation) with quantized angular momentum.
Ln mvr n
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.
• Plan for Physics 320. – Test #1: Nuclear Atom, Wave/Particle Duality, Wave Packets – Test #2: Schroedinger Equation, Atomic & Solid-state Physics – Nuclear Physics, Relativity
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.
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:
1
12
1 12
1 22
R
3 (1.097 107 m1 ) 4
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.
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