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Physics 2D Lecture Slides Feb 5 Vivek Sharma UCSD Physics - - PowerPoint PPT Presentation
Physics 2D Lecture Slides Feb 5 Vivek Sharma UCSD Physics - - PowerPoint PPT Presentation
Physics 2D Lecture Slides Feb 5 Vivek Sharma UCSD Physics Continuous & discrete spectra of Elements Visible Spectrum of Sun Through a Prism Emission & Absorption Line Spectra of Elements Kirchhoff Experiment : D Lines in Na
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Visible Spectrum of Sun Through a Prism
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Emission & Absorption Line Spectra of Elements
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Kirchhoff’ Experiment : “D” Lines in Na
D lines darken noticeably when Sodium vapor introduced Between slit and prism
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Emission & Absorption Line Spectrum of Elements
- Emission line appear dark
because of photographic exposure
Absorption spectrum of Na While light passed thru Na vapor is absorbed at specific λ
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Spectral Observations : series of lines with a pattern
- Empirical observation (by trial & error)
- All these series can be summarized in a simple formula
2 2 7 1
1 1 , , 1,2,3,4.. Fitting to spectral line series R=1 da .09737 10 ta
f i i f i
R n n n n n m λ
−
= > = − ×
How does one explain this ?
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Rutherford Atom & Classical Physics
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Atom: The Classical disaster
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Bohr’s Bold Model of Atom: Semi Quantum/Classical
1. Electron in circular orbit around proton with vel=v 2. Only stationary orbits allowed . Electron does not radiate when in these stable (stationary) orbits 3. Orbits quantized:
– Mev r = n h/2π (n=1,2,3…)
4. Radiation emitted when electron “jumps” from a stable orbit of higher energy stable orbit of lower energy Ef-Ei = hf =hc/λ 5. Energy change quantized
- f = frequency of radiation
F V
me
+e
r
- e
2 2
( ) 1 2
e
e U r k r KE m v = − =
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Reduced Mass of 2-body system
- Both Nucleus & e- revolve around their common center of mass (CM)
- Such a system is equivalent to single particle of “reduced mass” µ that
revolves around position of Nucleus at a distance of (e- -N) separation
µ= (meM)/(me+M), when M>>m, µ=m (Hydrogen atom) Νot so when calculating Muon (mµ= 207 me) or equal mass charges rotating around each other (similar to what you saw in gravitation)
me me
+Ze
r
- e
+ CM
F V
me
+e
r
- e
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Allowed Energy Levels & Orbit Radii in Bohr Model
2 2 2 2 2 2 2 2
E=KE+U = Force Equality for Stable Orbit Coulomb attraction = CP Force Total Energy E = KE+U= Negative E Bound sy
- stem
T 1 2 h 2 2 i 2 s
e e e
e k r m v e k r r e m v k r m v e KE k r − ⇒ ⇒ ⇒ = = = much energy must be added to the system to break up the bound atom
2 2 2 2 2 10 2 2 2 2
, 1 ,2 Radius of Electron Orbit : , 1 substitute in KE= 2 2 1 B 1 0.529 10 Quantized orbits of rotat
- hr Radius
In ge ,.... ; 1 ,2,... neral . io
n n e
n r mvr n a m mk n v mr r ke m v r n n n a n e e mk a
−
= ⇒ = = ⇒ = ⇒ = = ∞ = = = × ∞ =
- n
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Energy Level Diagram and Atomic Transitions
2 2 2 2 2 2 2 2 2 2 2 2 2 2 i
2 since , n =quantum number Interstate transition: 1 1 2 1 1 1 2 13.6 , 1, 2, 3.. 2 1 1 2 n
n n f i n f f f i i i f
ke E K U r ke f ha n n f ke c hca ke E eV n a n n ke n r a n a n E h n E n f E n λ − = = − = ∞ − = − = − = = − − = + = = → ∆ = = −
2 2
1 1 R =
f i
n n −
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Hydrogen Spectrum: as explained by Bohr
Bohr’s “R” Same as the Rydberg Constant derived emperically from Spectral series
2 2 2
2
n
ke Z E a n = −
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Another Look at the Energy levels
2 2 2
2
n
ke Z E a n = −
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Bohr’s Atom: Emission & Absorption Spectra
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Some Notes About Bohr Like Atoms
- Ground state of Hydrogen atom (n=1) E0= -13.6 eV
- Method for calculating energy levels etc applies to all Hydrogen-
like atoms -1e around +Ze
– Examples : He+, Li++
- Energy levels would be different if replace electron with Muons
- Bohr’s method can be applied in general to all systems under a
central force (e.g. gravitational instead of Coulombic)
1 2 1 2
If change ( ) Changes every thing: E, r , f etc "Importance of constants in your life" Q Q M M U r k G r r = →
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Atomic Excitation by Electrons: Franck-Hertz Expt
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