Lecture-2: Atomic Structure
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Transcript Lecture-2: Atomic Structure
Lecture-2
Bohr Model and Quantum
Theory
Bohr Atom
The Planetary Model of the Atom
Bohr’s
Bohr’sModel
Model
Nucleus
Electron
Orbit
Energy Levels
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.
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
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.
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.
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.
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.
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.
nh
mvr
2
Bohr Model (1913)
• Equations derived from Bohr’s Assumption
• Radius of the orbit
2
2
h
n ao
ao 2 2
rn
4 me
Z
h = Planck’s constant
n = orbit number
m = mass of electron
Z = atomic number e = charge on electron
r3
r2
r1
n=1 n=2
n=3
Bohr Model (1913)
2
For H: r1 1 a o a o
1
22 ao
r2
4a o
1
Called Bohr radius
For He+ (also 1 electron)
12 a o
1
r1
a o Smaller value for the radius.
2
2
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.
Bohr Model (1913)
Which of the following has the smallest
radius?
A) First excited state of H
B) Second excited state of He+
C) First excited state of Li+2
D) Ground state of Li+2
E) Second excited state of H
Bohr Model (1913)
Which of the following has the smallest
radius?
2
A)
B)
C)
D)
E)
2 ao
r2
4a o
First excited state of H
1
2
3
ao
9
+
ao
Second excited state of He r3
2
2
2
2 ao
4
+2
r2
ao
First excited state of Li
32
3
1 ao
1
+2
r1
ao
Ground state of Li
3
3
2
3
ao
Second excited state
of
H
r3
9a o
1
Problem
Calculate the radius of 5th orbit of the hydrogen atom.
n 2h 2
rn 2
4 Zme 2
n=5
h= 6.62 x 10-34 J sec
m=9.109x10-31kg
e=1.602x10-19C
π=3.14
Z=1
r = 13.225x10-10m
5
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.
Bohr Model (1913)
• Energy of the Electron
Z 2
E n A 2
n
constant, A = 2.18 x 10-18 J
12
E 1 A 2 A
1
12
1
E 2 A 2 A
4
2
12
1
E 3 A 2 A
9
3
E 0 (have formed ion)
What’s 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.
Bohr Model (1913)
E1 A
A
E2
4
+ sign shows
that energy was
absorbed.
A
3
E = E 2 - E 1 (A) = + A
4
4
x J) = 1.64 x 10-18 J
What is E when electron moves from n = 2 to n = 1?
A
3
E = E 1 - E 2 A ( )= - A
4
4
x J) = - 1.64 x 10-18 J
So: Ephoton = |E|transition = h = h(c/)
h = Planck’s constant = 6.62 x 10-34 J sec
c = speed of light = 3.00 x 108 m/sec
1
1
E = - A 2 2
n i
n f
When E is positive, the photon is absorbed
When E is negative, the photon is emitted
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)
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.
h where h = Planck’s constant
v = velocity
mv
m = mass
What is the in nm associated with a ping
pong ball (m = 2.5 g) traveling at 35.0
mph.
A) 1.69 x 10-32
B) 1.7 x 10-32
C) 1.69 x 10-22
D) 1.7 x 10-23
kg m2
6.62x10
s
2
h
s
1.69 x1032 m 1.7 x1023 nm
1kg 35.0 mi. 1.609 km 1000 m 1hr
mv
2.5g
1000g
hr
mi
km
3600s
34
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.
b)
m= 149g= 0.149kg
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