Bohr Model and Quantum Theory

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Bohr Model and Quantum Theory
Lecture-2
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Bohr Atom
The Planetary Model of the Atom
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Bohrs Model
Bohrs Model
Nucleus
Electron
Orbit
Energy Levels
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Photons
Max Planck (1858-1947)
Max Planck in 1900 stated that the light emitted
by a hot object (black body radiation) is given
off in discrete units or quanta. The higher the
frequency of the light, the greater the energy
per quantum.
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Frequency

• (a) and (b) represent two waves that are
  traveling at the same speed.
• In (a) the wave has long wavelength and low
  frequency
• In (b) the wave has shorter wavelength and higher
  frequency

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9-2. Photons
The system shown here detects people with fevers
on the basis of their infrared emissions, with
red indicating skin temperatures above normal.
In this way people with illnesses that may be
infectious can be easily identified in public
places.
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Photons
All the quanta associated with a particular
frequency of light have the same energy. The
equation is E hf where E energy, h
Planck's constant (6.63 x 10-34 J s), and f
frequency.
Electrons can have only certain discrete
energies, not energies in between.
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The Photoelectron Effect
The photoelectric effect is the emission of
electrons from a metal surface when light shines
on it. The discovery of the photoelectric effect
could not be explained by the electromagnetic
theory of light. Albert Einstein developed the
quantum theory of light in 1905.
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What is light?
Light exhibits either wave characteristics or
particle (photon) characteristics, but never both
at the same time. The wave theory of light and
the quantum theory of light are both needed to
explain the nature of light and therefore
complement each other.
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Bohr Model (1913)

• Assumptions
• 1) Only certain set of allowable circular orbits
  for an electron in an atom
• 2) An electron can only move from one orbit to
  another. It can not stop in between. So discrete
  quanta of energy involved in the transition in
  accord with Planck (E h?)
• 3) Allowable orbits have unique properties
  particularly that the angular momentum is
  quantized.

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Energy of photon, Ehv
 
 
 
 
In case of particle,
In circles the circumference (boundary of circle)
is
According wave model of atom,
 
 
Angular momentum,
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Bohr Model (1913)

• Equations derived from Bohrs Assumption
• Radius of the orbit

r3
r2
h Plancks constant m mass of electron e
charge on electron
r1
n orbit number Z atomic number
n1
n2
n3
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Bohr Model (1913)

• For H
• For He (also 1 electron)

Called Bohr radius
Smaller value for the radius.
This makes sense because of the larger charge in
the center
For H and any 1 electron system
n 1 called ground state
n 2 called first excited state
n 3 called second excited state etc.
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Bohr Model (1913)

• Which of the following has the smallest radius?
• First excited state of H
• Second excited state of He
• First excited state of Li2
• Ground state of Li2
• Second excited state of H

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Bohr Model (1913)

• Which of the following has the smallest radius?
• First excited state of H
• Second excited state of He
• First excited state of Li2
• Ground state of Li2
• Second excited state of H

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Problem
Calculate the radius of 5th orbit of the
hydrogen atom.
n5 h 6.62 x 10-34 J sec m9.109x10-31kg e1.602x
10-19C p3.14 Z1
r5 13.225x10-10m
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9-9. The Bohr Model
Electron orbits are identified by a quantum
number n, and each orbit corresponds to a
specific energy level of the atom. An atom having
the lowest possible energy is in its ground
state an atom that has absorbed energy is in an
excited state.
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Bohr Model (1913)

• Energy of the Electron

 
constant, A 2.18 x 10-18 J
Whats happening to the energy of the orbit as
the orbit number increases?
Energy is becoming less negative, therefore it
is increasing. The value approaches 0.
Completely removed the electron from the atom.
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Bohr Model (1913)

sign shows that energy was absorbed.
??????????????x???????J) 1.64 x 10-18 J
What is ?E when electron moves from n 2 to n
1?
????????????????x???????J) - 1.64 x 10-18 J
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• So Ephoton ?Etransition h? h(c/?)
• h Plancks constant 6.62 x 10-34 J sec
• c speed of light 3.00 x 108 m/sec
• When ?E is positive, the photon is absorbed
• When ?E is negative, the photon is emitted

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Problem
A green line of wavelength 4.86x107 m is observed
in the emission spectrum of hydrogen. a)
Calculate the energy of one photon of this green
light. b) Calculate the energy loses by the one
mole of H atoms.
Solution We know the wavelength of the light, and
we calculate its frequency so that we can then
calculate the energy of each photon.
a)
b)
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• What is the wavelength of the photon needed to
  move an electron from n 1 to n 2 in the H
  atom?
• recall h 6.62 x 10-34J sec, ?? c
• 1.64 x 10-18 m
• 2.47 x 1015 m
• 6.62 x 10-34 m
• 1.21 x 10-7 m
• 2.18 x 10-18 m

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• What is the wavelength of the photon needed to
  move an electron from n 1 to n 2 in the H
  atom?

So, light with this wavelength is absorbed
When the electron goes back to n 1, light with
the same energy and wavelength will be emitted.
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• Ionization Energy
• energy needed to remove the outermost electron
  from an atom in its ground state.
• For Helectron moves from n 1 to n 8
• E8 0, E1 - 2.18 x 10-18 J
• Therefore, the ionization energy for H is
• 2.18 x 10-18 J

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• DeBroglie Postulate (1924)
• Said if light can behave as matter, i.e. as a
  particle, then matter can behave as a wave. That
  is, it moves in wavelike motion.
• So, every moving mass has a wavelength (?)
  associated with it.
• where h Plancks constant
• v velocity
• m mass

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• What is the ??in nm associated with a ping pong
  ball (m 2.5 g) traveling at 35.0 mph.
• 1.69 x 10-32 B) 1.7 x 10-32
• C) 1.69 x 10-22 D) 1.7 x 10-23

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Problem
(a)Calculate the wavelength in meters of an
electron traveling at 1.24 x107 m/s. The mass of
an electron is 9.11x 10-28 g. (b) Calculate
the wavelength of a baseball of mass 149g
traveling at 92.5 mph. Recall that 1 J 1
kgm2/s2.
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b)
m 149g 0.149kg
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• Heisenberg Uncertainty Principle
• To explain the problem of trying to locate a
  subatomic particle (electron) that behaves as a
  wave
• Anything that you do to locate the particle,
  changes the wave properties
• He said It is impossible to know
  simultaneously both the momentum(p) and the
  position(x) of a particle with certainty

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Thats all for today