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Rutherford Model
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J.J. Thomson Model
Atom consists of positively charged matter with electron embedded on it
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-Positively charged matter
Geiger and Masden Experiment
Some alpha particles are deflected=> There must be a very heavy particles,Þ It can not be electrons because alpha particle mass is about 8000 times mass.
Rutherford Model
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Rutherford Scattering
Remember some formulas
x
𝑥 /sin𝜃=𝑦 /sin𝛼
y
𝑝1
𝑝2p
sin 12(𝜋−𝜃 )=cos 𝜃2
Δ𝑝=𝑝1−𝑝2=∫𝐹 𝑑𝑡Angular momentum:
Electric Force Between alpha particles and nucleus
𝐹=1
4 𝜋 𝜀02𝑍𝑒2
𝑟2
Nuclear DimensionsRutherford assumed the nucleus size is smaller compared to the minimum distance of alpha particles approaches nucleus before deflected
At closest point R, all kinetic particles is converted to electric potential energy
KE
R is ussually predicted as maximum the nucleus size
Fraction of incident alpha scattered by or more
𝑓 =𝜋𝑛𝑡 [ 𝑍𝑒24𝜋𝜖0𝐾𝐸 ]
2
cot 2 𝜃2
Number of alpha particle per unit are striking screen at
N
Weakness of Rutherford Model
+Ze
-e
Electron Orbit
Condition for a dynamically stable orbit of hidrogen atom
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-ev
r
𝑣=𝑒
√4𝜋 𝜀0𝑚𝑟
Total Energy
E = EK +EP
Bohr ModelAn electron can circle a nucleus only if its orbit contains an integral number of de Broglie wavelenghts
𝜆= h𝑚𝑣= h𝑒 √ 4𝜋 𝜀0𝑟𝑚
Condition for orbit stability 𝑛𝜆=2𝜋𝑟𝑛
Orbital radii in Bohr atom 𝑟𝑛=𝑛2h2𝜀0𝜋𝑚𝑒2
𝑎0=𝑟1=h2𝜀0𝜋𝑚𝑒2
=5.292×10−11mBohr radius
Energy levels 𝐸𝑛=𝑚𝑒4
8 𝜀02h2
1𝑛2
=𝐸1
𝑛2
𝐸1=−13.6𝑒𝑉=−2.18×10− 18 𝐽
Atomic Spectra
Ground state
excitation
hfemission
Source: www.cfa.harvard.edu
Source: 5e.plantyphys.net
Hydrogen Series1𝜆=−
𝐸1
h𝑐 ( 1𝑛𝑓2 −
1𝑛𝑖2 )
− 𝐸1h𝑐 =𝑅=1.097×107/mRydberg constant:
Lyman Series: 1𝜆=−
𝐸1
h𝑐 ( 112− 1𝑛𝑖2 ) 𝑛𝑖=2,3,4 ,…
Balmer Series:
Pachen Series
Bracket Series
Pfund Series
1𝜆=−
𝐸1
h𝑐 ( 122 − 1𝑛𝑖2 )
1𝜆=−
𝐸1
h𝑐 ( 132 − 1𝑛𝑖2 )
1𝜆=−
𝐸1
h𝑐 ( 142− 1𝑛𝑖2 )
1𝜆=−
𝐸1
h𝑐 ( 152− 1𝑛𝑖2 )
𝑛𝑖=3,4,5 ,…
𝑛𝑖=4,5 ,6…
𝑛𝑖=5 ,6 ,7…
𝑛𝑖=6 ,7,8 ,…
Source: www. astro.cornell.edu
Source: chemed.chem.purdue.edu
High voltage+
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Light Interaction with atom
hf
absoption
hf
Spontaneous emission
hf
Stimulated emission
hf
hf
Stimulated emission
Laser (Light amplification by stimulated emission of radiation)
Population inversionfast decay
hf hf
www.photon-science.desy.de
www.ryerson.ca
He-Ne Laser
Source: hyperphysics.phy-astr.gsu.edu
Source: www.rp-photonics.com
Semiconductor Laser
Surce: www.sony.net