•THE BOHR MODEL OF THE ATOM

October 23, 2009

The Bohr Model of Hydrogen Atom

Light absorbed or emitted is from electrons moving between energy levels

Only certain energies are observedTherefore, only certain energy levels exist

Energy levels are Quantized

Energy Adsorption/EmissionEnergy Adsorption/Emission

Absorption and Emission Spectra

Hydrogen Energy Levels

Constant = Rhc = 2.18 x 10-18 JR = Rydberg constant = 1.0974 x 107 m-1

h = Planck’s constant = 6.626 x 10-34 Jsc= velocity of light in vacuum = 3.0 x 108 m/s

En Constant

n2

Each line corresponds to a transition:

Example: n=3 n = 2

En 2.18 x 10-18 J

n2

E photon h hc

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E3 = −2.18 x 10-18 J

32= −2.42x10−19J

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E2 = −2.18 x 10-18 J

22= −5.45x10−19J

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hc

E photon

=(6.626x10−34 J ⋅s)(3.0x108m /s)

−3.03x10−19J= −6.56x10−7m = 656nm

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E photon = ΔE = E final − E initial = E2 − E3

= −5.45x10−19J − (−2.42x10−19J) = − 3.03x10−19J

Balmer seriesBalmer series

Explanation of line spectra

The emission line with the shortest wavelength is:

1. 12. 23. 34. 45. 5

The emission line with the longest wavelength is:

1. 12. 23. 34. 45. 5

The emission line with the highest energy is:

1. 12. 23. 34. 45. 5

The absorption line with the shortest wavelength is:

1. 12. 23. 34. 45. 5

The absorption line with the lowest energy is:

1. 12. 23. 34. 45. 5

A Revolutionary Idea: Matter Waves

All matter acts as particles and as waves.Macroscopic objects have tiny waves- not observed.

Wave nature only becomes apparent when object is VERY lightFor electrons in atoms, wave properties are important.deBroglie Equation:

h

mv

Matter waves- Examples

Macroscopic object: 200 g rock travelling at 20 m/s has a wavelength:

Electron inside an atom, moving at 40% of the speed of light (0.4 x 3x108m/s):

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h

m ⋅v=6.626x10−34 J ⋅s

(0.2kg)(20m /s)=1.66x10−34m

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=h

m ⋅v=

6.626x10−34 J ⋅s

(9.11x10−31kg)(0.4)(3.0x108m /s)= 6.06x10−12m = 0.006nm

Can see matter waves in experiments