Download File - Mr. C at Hamilton

Electromagnetic Spectrum Calculations
Using Planck’s Constant…
Determining the Speed of Light
• Galileo tried
unsuccessfully to
determine the speed of
light using an assistant
with a lantern on a
distant hilltop.
Light travels through empty space at a speed
of 300,000 km/s (300,000,000 m/s)
• In 1676, Danish astronomer
Olaus Rømer discovered that
the exact time of eclipses of
Jupiter’s moons depended on
the distance of Jupiter to Earth
• This happens because it takes
varying times for light to travel
the varying distance between
Earth and Jupiter
• Using d=rt with a known
distance and a measured time
gave the speed (rate) of the
light
Light is electromagnetic radiation and is
characterized by its wavelength ()
The Nature of Light
• In the 1860s, the Scottish mathematician and physicist James
Clerk Maxwell succeeded in describing all the basic properties
of electricity and magnetism in four equations.
• This mathematical achievement demonstrated that electric
and magnetic forces are really two aspects of the same
phenomenon, which we now call electromagnetism.
The Nature of Light
• First durable color photographic image, demonstrated by
James Clerk Maxwell in an 1861 lecture.
• (It’s a tartan.
The Nature of Light
• In the 1860s, the Scottish mathematician and physicist James
Clerk Maxwell succeeded in describing all the basic properties
of electricity and magnetism in four equations.
• This mathematical achievement demonstrated that electric
and magnetic forces are really two aspects of the same
phenomenon, which we now call electromagnetism.
• Because of its electric and
magnetic properties, light
is also called
electromagnetic
radiation.
• Visible light falls in the 400
to 700 nm range.
• Stars, galaxies and other
objects emit light in all
wavelengths.
Light has properties of both
waves and particles
• Newton thought light was in the form of little packets of energy
called photons and subsequent experiments with blackbody
radiation indicate it has particle-like properties.
• Young’s Double-Slit Experiment indicated light behaved as a wave.
• Light has a dual personality; it behaves as a stream of particle like
photons, but each photon has wavelike properties.
Wavelength and Frequency
wavelength ()
amplitude
peak
Spectral lines are produced when an electron jumps from
one energy level to another within an atom
• The nucleus of an atom is
surrounded by electrons that
occupy only certain orbits or
energy levels
• When an electron jumps from
one energy level to another, it
emits or absorbs a photon of
appropriate energy (and hence
of a specific wavelength).
• The spectral lines of a particular
element correspond to the
various electron transitions
between energy levels in atoms
of that element.
• Bohr’s model of the atom
correctly predicts the
wavelengths of hydrogen’s
spectral lines.
Spectral lines?
The equation for this?
2.178  10
En 
2
n
18
Who was Max Planck?
•In 1900, German physicist Max Planck , “the founder of
the quantum theory”,(1858-1947) was trying to model
the broad smooth spectrum of electromagnetic radiation
(i.e., light) emitted by a warm body.
•This “black body radiation” is what you see coming from
the sun, the filament of an incandescent light bulb, or a
hot electric stove element.
•Its ‘spectrum’, the range of frequencies making up the
radiation, is readily displayed by a prism or a diffraction
grating.
•In explaining the shape of the black body spectrum,
Planck assumed that the electromagnetic radiation
came not in continuous waves of energy, but in discrete
clumps of energy which we now call photons.
•Planck postulated the ‘photons’, at each frequency
have a discreteA energy.
E = hf, where E is the energy of the photon in Joules, f is
the frequency in Hertz, and h is Planck’s constant.
Picture credit:
http://en.wikipedia.org/wiki/File:Max_Planck.png
A. distinct,
unique
separate,
Black Body Radiation
• The radiation has a specific spectrum and intensity that
depends only on the temperature of the body.
Black Body Radiation
• The radiation has a specific spectrum and intensity that
depends only on the temperature of the body.
Who was Max Planck?
•The existence of a smallest unit of light
energy is one of the foundations of
quantum mechanics.
•The symbol (h) is used to denote
Planck’s constant, which he discovered
in 1899. It is used as a proportionality
constant between the energy and
frequency of an electromagnetic wave.
(NOTE: We use it to describe the energy
of a photon.)
• h = 6.626 x 10-34 Js (joule seconds)
If you need more than this, go here:
http://web.mit.edu/lululiu/Public/pixx/not-pixx/photoelectric.pdf
Picture credit:
http://en.wikipedia.org/wiki/File:Max_Planck.png
Important Equations and their
units
•
The Nature of Light – Einstein
•
(style)
Planck’s Practice Problems
1. When we see light from a neon sign, we are observing radiation
from excited neon atoms. If this radiation has a wavelength of 640
nm, what is the energy of the photon being emitted?
Planck’s Practice Problems
1. When we see light from a neon sign, we are observing radiation
from excited neon atoms. If this radiation has a wavelength of 640
nm, what is the energy of the photon being emitted?
A. Pick your equation!
Planck’s Practice Problems
1. When we see light from a neon sign, we are observing radiation
from excited neon atoms. If this radiation has a wavelength of 640
nm, what is the energy of the photon being emitted?
A. Pick your equation!
B. E=hν or E=hc/λ
Planck’s Practice Problems
1. When we see light from a neon sign, we are observing radiation
from excited neon atoms. If this radiation has a wavelength of 640
nm, what is the energy of the photon being emitted?
A. Pick your equation!
B. E=hν or E=hc/λ
You know me, I like this one: E=hc/λ
Planck’s Practice Problems
1. When we see light from a neon sign, we are observing radiation
from excited neon atoms. If this radiation has a wavelength of 640
nm, what is the energy of the photon being emitted?
A. Pick your equation!
B. E=hν or E=hc/λ
You know me, I like this one: E=hc/λ
C. E=(6.626×10-34Js)(3.00×108m/s) / 640x10-9m
(or you can use: 6.40x10-7m)
Planck’s Practice Problems
1. When we see light from a neon sign, we are observing radiation
from excited neon atoms. If this radiation has a wavelength of 640
nm, what is the energy of the photon being emitted?
A. Pick your equation!
B. E=hν or E=hc/λ
You know me, I like this one: E=hc/λ
C. E=(6.626×10-34Js)(3.00×108m/s) / 640x10-9m
(or you can use: 6.40x10-7m)
E=
-19
3.11x10 J
Planck’s Practice Problems
2. Light with a wavelength of 614.5 nm looks orange. What is the
energy, in joules, of a photon of this orange light?
A. Pick your equation!
Planck’s Practice Problems
2. Light with a wavelength of 614.5 nm looks orange. What is the
energy, in joules, of a photon of this orange light?
A. Pick your equation!
B. E=hν or E=hc/λ
You know me, I like this one: E=hc/λ
Planck’s Practice Problems
2. Light with a wavelength of 614.5 nm looks orange. What is the
energy, in joules, of a photon of this orange light?
A. Pick your equation!
B. E=hν or E=hc/λ
You know me, I like this one: E=hc/λ
C. E=(6.626×10-34Js)(3.00×108m/s) / 614.5x10-9m
(or you can use: 6.145x10-7m)
Planck’s Practice Problems
2. Light with a wavelength of 614.5 nm looks orange. What is the
energy, in joules, of a photon of this orange light?
A. Pick your equation!
B. E=hν or E=hc/λ
You know me, I like this one: E=hc/λ
C. E=(6.626×10-34Js)(3.00×108m/s) / 614.5x10-9m
(or you can use: 6.145x10-7m)
E=
-19
3.23x10 J
Planck’s Practice Problems
3. A photon of light produced by a surgical laser has an energy of
3.027 x 10 -19J. Calculate the frequency and the wavelength of the
photon.
A. Pick your equation!
Planck’s Practice Problems
3. A photon of light produced by a surgical laser has an energy of
3.027 x 10 -19J. Calculate the frequency and the wavelength of the
photon.
A. Pick your equation!
B. E=hν or E=hc/λ
Umm, I like things easy so I’ll use this one: E=hν
Planck’s Practice Problems
3. A photon of light produced by a surgical laser has an energy of
3.027 x 10 -19J. Calculate the frequency and the wavelength of the
photon.
A. Pick your equation!
B. E=hν or E=hc/λ
Umm, I like things easy so I’ll use this one: E=hν
C. 3.027 x 10 -19J =(6.626×10-34Js)v
Planck’s Practice Problems
3. A photon of light produced by a surgical laser has an energy of
3.027 x 10 -19J. Calculate the frequency and the wavelength of the
photon.
A. Pick your equation!
B. E=hν or E=hc/λ
Umm, I like things easy so I’ll use this one: E=hν
C. 3.027 x 10 -19J =(6.626×10-34Js)v
D. v=(3.027 x 10 -19J)/(6.626×10-34Js)
Planck’s Practice Problems
3. A photon of light produced by a surgical laser has an energy of
3.027 x 10 -19J. Calculate the frequency and the wavelength of the
photon.
A. Pick your equation!
B. E=hν or E=hc/λ
Umm, I like things easy so I’ll use this one: E=hν
C. 3.027 x 10 -19J =(6.626×10-34Js)v
D. v=(3.027 x 10 -19J)/(6.626×10-34Js)
v= 4.568x1014Hz
(or 4.568x1014/s or 4.568x1014s -1)
Planck’s Practice Problems
3. A photon of light produced by a surgical laser has an energy of
3.027 x 10 -19J. Calculate the frequency and the wavelength of the
photon.
A. Pick your equation!
B. E=hν or E=hc/λ
Umm, I like things easy so I’ll use this one: E=hν
C. 3.027 x 10 -19J =(6.626×10-34Js)v
D. v=(3.027 x 10 -19J)/(6.626×10-34Js)
E. v=4.568x10-19s -1
Now what?
Solve for wavelength!
Planck’s Practice Problems
3. A photon of light produced by a surgical laser has an energy of
3.027 x 10 -19J. Calculate the frequency and the wavelength of the
photon.
A. Pick your equation!
B. E=hν or E=hc/λ
Umm, I like things easy so I’ll use this one: E=hν
C. 3.027 x 10 -19J =(6.626×10-34Js)v
D. v=(3.027 x 10 -19J)/(6.626×10-34Js)
E. v=4.568x10-19s -1
Now what?
Solve for wavelength!
F. c = λν or λ = c/ν
Planck’s Practice Problems
3. A photon of light produced by a surgical laser has an energy of
3.027 x 10 -19J. Calculate the frequency and the wavelength of the
photon.
A. Pick your equation!
B. E=hν or E=hc/λ
Umm, I like things easy so I’ll use this one: E=hν
C. 3.027 x 10 -19J =(6.626×10-34Js)v
D. v=(3.027 x 10 -19J)/(6.626×10-34Js)
E. v=4.568x10-19s -1
Now what?
Solve for wavelength!
F. c = λν or λ = c/ν
G. λ=(3.00×108m/s) / 4.568x10-19s -1
Planck’s Practice Problems
3. A photon of light produced by a surgical laser has an energy of
3.027 x 10 -19J. Calculate the frequency and the wavelength of the
photon.
A. Pick your equation!
B. E=hν or E=hc/λ
Umm, I like things easy so I’ll use this one: E=hν
C. 3.027 x 10 -19J =(6.626×10-34Js)v
D. v=(3.027 x 10 -19J)/(6.626×10-34Js)
E. v=4.568x10-19s -1
Now what?
Solve for wavelength!
F. c = λν or λ = c/ν
G. λ=(3.00×108m/s) / 4.568x10-19s -1
λ=6.567 x 10-7m or 656.7 x10-9m
~λ=657nm
Planck’s Practice Problems
3. A photon of light produced by a surgical laser has an energy of
3.027 x 10 -19J. Calculate the frequency and the wavelength of the
photon.
A. Pick your equation!
B. E=hν or E=hc/λ
Umm, I like things easy so I’ll use this one: E=hν
C. 3.027 x 10 -19J =(6.626×10-34Js)v
D. v=(3.027 x 10 -19J)/(6.626×10-34Js)
E. v=4.568x10-19s -1
Now what?
Solve for wavelength!
F. c = λν or λ = c/ν
G. λ=(3.00×108m/s) / 4.568x10-19s -1
λ=6.567 x 10-7m or 656.7 x10-9m
~λ=657nm
For funsies
• Why is the sky blue?
• Why are sunsets red?
For funsies
• Why is the sky blue?
• Why are sunsets red?
• Blue is scattered more than other colors because it travels as
shorter, smaller waves.
• As the sunlight has passed through all this air, the air molecules
have scattered and rescattered the blue light many times in many
directions.
• BUT…
• The surface of Earth has reflected and scattered the light. All this
scattering mixes the colors back together again so we see more
white and less blue.
For funsies
• Why is the sky blue?
• Why are sunsets red?
• At sunset, even more of the blue light is scattered, allowing the
reds and yellows to pass straight through to your eyes.