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

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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