Lecture 20 10/19/05

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Lecture 20



10/19/05

wavelength

wavelength

Amplitude

Node

Electromagnetic Radiation (Light as waves)

Moving Waves

c =
λν


c = speed of light (3 x 10
8

m/s in a vacuum)

λ

= wavelength (m)

ν

= frequency (s
-
1

or Hertz, Hz)

Electromagnetic Radiation

Red light has


= 700 nm. Calculate the
frequency.

Freq
=

3.00 x 10
8
m/s
7.00 x 10
-7
m

4.29 x 10
14
sec
-1
700

nm



1 x 10
-9
m
1 nm

=
7.00 x 10
-7
m
Standing
(stationary) Waves



Has 2 or more nodes


Distance between
nodes is
λ
/2.



Distance between ends
has to be n(
λ
/2)

a)
Draw a standing wave with 1 node. What is the wavelength of this
wave?

b)
Draw a standing wave with 3 nodes between the ends. What is the
wavelength?

c)
If the wavelength of the standing wave is 2.5 cm, how many waves
fit within the boundaries? How many nodes?


Visible Light


1.
Which color in the visible spectrum has the highest frequency?


2.
Is the wavelength of x
-
rays longer or shorter than UV?


The frequency of radiation used in microwave
ovens is 2.45 GHz (1 gigahertz is 10
9

s
-
1
.


What is the wavelength in nm of this radiation?

Light as particles



Max Planck
-


Vibrations are quantized


Planck’s constant


E=h
ν

= hc/
λ


E = energy (J)


h = Planck’s constant


6.626 x 10
-
34

J
-
s


Photoelectric Effect

Photoelectric Effect

Classical theory said that Energy of ejected electron
should increase with increase in light intensity


NOT OBSERVED

No e
-

observed until light of a certain minimum E is used

Number of e
-

ejected depends on light intensity.

Light consists of particles called PHOTONS of discrete energy.

Photoelectric Effect

E
electron
= E
light

-

E
ejection

Compare the energy of a mole of red light photons
(
λ
= 700 nm) and a mole of UV photons (
λ
= 300 nm)



KJ/mol

1
.
399
J/mole

399126
E
e)
photon/mol

10
02
.
6
(
photon
/
J
10
62
.
6
E
nm
10
m

1
)
nm

300
(
)
s
m
10
00
.
3
)(
s
J
10
63
.
6
(
E
23
19
9
8
34





















λ
hc
h
ν
E


KJ/mol

171
J/mole
054
171
E
e)
photon/mol

10
02
.
6
(
photon
/
J
10
84
.
2
E
nm
10
m

1
)
nm

700
(
)
s
m
10
00
.
3
)(
s
J
10
63
.
6
(
E
23
19
9
8
34





















λ
hc
h
ν
E
Dual Nature of Light

Both wave and particle characteristics


Wave


Refraction


Diffraction

Particle


Photoelectric effect

Diffraction

Light bends as it moves through a slit or around
a boundary






Refraction

Bending of light as it passes between materials of
different optical density.

Line Emission Spectrum

“Excited” atoms emit light

Line Emission Spectrum

Balmer series


1
7
2
2
m
10
0974
.
1
)
t
tan
cons

Rydberg
(

R
2
n

where
integer,

an

is

n

n
1
2
1
R
λ
1












Rydberg equation

Balmer Series

Atomic Spectra and Bohr


1.

Any orbit should be possible and so is any energy.

2.

But a charged particle moving in an electric field
should emit energy.

Electron would eventually run out of energy

Bohr

New theory :
Quantum

or
Wave Mechanics


e
-

can only exist in certain discrete orbits


Stationary states


e
-

is restricted to
QUANTIZED

energy states.

level
energy
n
light

of

speed

c
constant

s
Planck'
h
m
10
0974
.
1
constant

Rydberg
R
n
Rhc
E
n
1
n
1
hcR
n
1
n
1
R
hc
λ
1
hc
λ
hc
E

n
1
n
1
R
λ
1
7
2
n
2
2
2
1
2
2
2
1
2
2
2
1






















































n= principal quantum number


n is an integer


n with the lowest possible energy is said to
be in the
ground state



Electrons with higher energy than ground
state are said to be in an
excited state

Calculate the energies of n=1, n=2, and
n=3 states of the hydrogen atom in
J/atom.


R = 1.097 x 10
7

m
-
1

h = 6.626 x 10
-
34

J
-
s

c = 2.998 x 10
8

m/s

s
/
m
10
998
.
2
light

of

speed

c
s
J
10
62
.
6
constant

s
Planck'
h
m
10
0974
.
1
constant

Rydberg
R
2
n

and

1
n

n
1
n
1
Rhc
n
Rhc
n
Rhc
E
E
E
8
34
7
2
initial
2
final
2
initial
2
final
initial
final














































Moving between energy levels

Calculate the wavelength of the green
light of excited H atoms.