• Study Resource
• Explore

Survey

* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project

Document related concepts

Theoretical and experimental justification for the Schrödinger equation wikipedia, lookup

Double-slit experiment wikipedia, lookup

Bohr–Einstein debates wikipedia, lookup

Wave–particle duality wikipedia, lookup

X-ray fluorescence wikipedia, lookup

Atomic theory wikipedia, lookup

Ultrafast laser spectroscopy wikipedia, lookup

Rutherford backscattering spectrometry wikipedia, lookup

Hydrogen atom wikipedia, lookup

Bohr model wikipedia, lookup

Electron scattering wikipedia, lookup

Atomic orbital wikipedia, lookup

Electron configuration wikipedia, lookup

Matter wave wikipedia, lookup

Elementary particle wikipedia, lookup

Tight binding wikipedia, lookup

Particle in a box wikipedia, lookup

Ionization wikipedia, lookup

X-ray photoelectron spectroscopy wikipedia, lookup

Atom wikipedia, lookup

Niels Bohr wikipedia, lookup

James Franck wikipedia, lookup

Transcript
```Lecture 15: Bohr Model of the
Atom
• Outline
– Emission spectrum of atomic hydrogen.
– The Bohr model.
– Extension to higher atomic number.
Light as Quantized Energy
• Comparison of experiment to the “classical”
prediction:
Classical prediction is
for significantly higher
intensity as smaller
wavelengths than what
is observed.
“The Ultraviolet Catastrophe”
Light as Quantized Energy
• Planck found that in order to model this behavior,
one has to envision that energy (in the form of
light) is lost in integer values according to:
DE = nhn
frequency
Energy Change
n = 1, 2, 3 (integers)
h = Planck’s constant = 6.626 x 10-34 J.s
Light as a ‘Particle’
• As frequency
of incident light is increased,
kinetic energy of emitted eincreases linearly.
0
1
2
men  hn photon  
2
n0
Frequency (n)

 = energy needed to release e-
Interference of Light
• Shine light through a crystal and look at pattern
of scattering.
• Diffraction can only be explained by treating light
as a wave instead of a particle.
Particles as waves
• Electrons shine through a crystal and look at pattern
of scattering.
• Diffraction can only be explained by treating electrons
as a wave instead of a particle.
Emission
Photon Emission
• Relaxation from one
energy level to another
by emitting a photon.
• With DE = hc/l
• If l = 440 nm,
DE= 4.5 x 10-19 J
Emission spectrum of H
“Quantized” spectrum
DE
DE
“Continuous” spectrum
Any DE is
possible
Only certain
DE are
allowed
Emission spectrum of H (cont.)
Light Bulb
Hydrogen Lamp
Quantized, not continuous
Emission spectrum of H (cont.)
We can use the emission spectrum to determine the
energy levels for the hydrogen atom.
Balmer Model
• Joseph Balmer (1885) first noticed that the
frequency of visible lines in the H atom spectrum
could be reproduced by:
1 1
n 2 2
2 n
n = 3, 4, 5, …..
• The above equation predicts that as n increases,
the frequencies become more closely spaced.


Rydberg Model
• Johann Rydberg extends the Balmer model by
finding more emission lines outside the visible
region of the spectrum:
 1
1 
n  Ry  2  2 
n1 n 2 
n1 = 1, 2, 3, …..
n2 = n1+1, n1+2, …
Ry = 3.29 x 1015 1/s
• This suggests that the energy levels of the H atom
are proportional to 1/n2
The Bohr Model
• Niels Bohr uses the emission spectrum of
hydrogen to develop a quantum model for H.
• Central idea: electron circles the “nucleus” in
only certain allowed circular orbitals.
• Bohr postulates that there is Coulombic attraction
between e- and nucleus. However, classical
physics is unable to explain why an H atom
doesn’t simply collapse.
The Bohr Model (cont.)
• Bohr model for the H atom is capable of
reproducing the energy levels given by the
empirical formulas of Balmer and Rydberg.
2 

Z = atomic number (1 for H)
Z
18
E  2.178x10 J 2 
n 
n = integer (1, 2, ….)
• Ry x h = -2.178 x 10-18 J (!)
The Bohr Model (cont.)
2 

Z
18
E  2.178x10 J 2 
n 

• Energy levels get closer together
as n increases
• at n = infinity, E = 0
The Bohr Model (cont.)
• We can use the Bohr model to predict what DE is
for any two energy levels
DE  E final  E initial
 1 
 1 
18
18
DE  2.178x10 J
n 2 
 (2.178x10 J)n 2 
 initial 
 final 

 1

1
DE  2.178x1018 J
n 2  n 2 

 final
initial 
The Bohr Model (cont.)
• Example: At what wavelength will emission from
n = 4 to n = 1 for the H atom be observed?
 1

1
DE  2.178x1018 J
n 2  n 2 

 final
initial 
1
4
 1 
DE  2.178x10 J1  2.04x1018 J
 16 
18

18

DE  2.04x10 J 
hc
l
l  9.74 x108 m  97.4nm
The Bohr Model (cont.)
• Example: What is the longest wavelength of light
that will result in removal of the e- from H?
 1

1
DE  2.178x1018 J
n 2  n 2 

 final
initial 
1



DE  2.178x1018 J0 1  2.178x1018 J
18
DE  2.178x10 J 
hc
l
l  9.13x108 m  91.3nm
Extension to Higher Z
• The Bohr model can be extended to any single
electron system….must keep track of Z
(atomic number).
2 

Z
18
E  2.178x10 J 2 
n 
Z = atomic number
n = integer (1, 2, ….)
• Examples: He+ (Z = 2), Li+2 (Z = 3), etc.
Extension to Higher Z (cont.)
• Example: At what wavelength will emission from
n = 4 to n = 1 for the He+ atom be observed?
 1

1
DE  2.178x1018 JZ 2 
n 2  n 2 

 final
initial 
2
1
4
 1 
DE  2.178x10 J41  8.16x1018 J
 16 
hc
18
l  2.43x108 m  24.3nm
DE  8.16x10 J 
l
l H  l He
18



Where does this go wrong?
• The Bohr model’s successes are limited:
• Doesn’t work for multi-electron atoms.
• The “electron racetrack” picture is incorrect.
• That said, the Bohr model was a pioneering,
“quantized” picture of atomic energy levels.
```
Related documents