Download Blackbody Radiation

Plan for Today (AP Physics 2)
• Questions on HW (due tomorrow)
• Notes/Lecture on Blackbody Radiation
Background
• Attempts to explain matter at the atomic
level with classical physics were
unsuccessful in the early 1900s
• Blackbody radiation (and problems
understanding it) actually led to quantum
physics
Background Information
• Thermal Radiation – electromagnetic
radiation an object will emit (at any
temperature)
• At low temperatures, mostly infrared
– Can’t see it, may feel it gives off heat
• As temperature increases, object glows
red, then appears to be white
• We actually have thermal radiation from
infrared, visible, and ultraviolet
More Background Information
• Blackbody – an ideal system that absorbs
ALL radiation incident on it
• No light is reflected – so it’s color is light
coming from it
• Approximation – small hole leading to inside
of a hollow object
– Radiation emitted through the hole depends only
on the temperature of the cavity walls and not
other factors
Picture of Blackbody
Approximation
As light bounces around
in the cavity, light gets
absorbed and it’s less
and less likely any light
will reflect back out of
the box
See how there’s less and less
light
Problem with Earlier
Explanations
• Looking at intensity and Rayleigh-Jean’s law, we
have intensity higher as frequency gets higher
• In fact, it predicts that the intensity of light at
high frequencies will get higher and higher and
the total energy radiated will approach infinity –
but this is impossible
• Great difference between theory and
experimental values in UV region
• It’s a catastrophe!
Intensity vs. Frequency and
Catastrophe
Intensity vs. Wavelength
Wien’s Displacement Law
• Radiated energy varies with temperature
and wavelength
• As temperature increases, total amount
of energy it emits (area under curve)
increases
• Peak of the distribution shifts to shorter
wavelengths
• Shift follows Wien’s displacement law
Wien’s Displacement Law
Wien’s Displacement
• Max Wavelength * T = 0.2898 * 10^-2
m*K
Max Planck and the UV
Catastrophe
• He was originally looking at light bulbs
and trying to figure out how to maximize
light and minimize the heat produced by
the filament
• Looked at the curve of Intensity vs.
wavelength for classical and real
Planck
• Came up with the idea that energy can’t
be arbitrary values
• Instead, energy is quantized
Plank’s Constant
In his studies of black-body radiation, Maxwell
Planck discovered that electromagnetic energy is
emitted or absorbed in discrete quantities.
Planck’s E = nhf
(h = 6.626 x 10-34 J s)
Equation: n is positive integer, f is frequency
Apparently, light consists of
tiny bundles of energy called
photons, each having a welldefined quantum of energy.
Photon
E = hf
Link to more information
Blackbody Spectrum
• PHET
Big Idea
• Quantized energy states
• Even Planck wasn’t so sure
– It was basically “hey, this makes the math
work”
• Einstein later figured out the “why”
Example Problem
• Temperature of the skin is about 35
degrees Celsius. At what wavelength
does the radiation emitted from the skin
reach its peak?
Answer
• 940 micrometers
Example Problem
• A 2.0 kg object is attached to a massless
spring with spring constant k = 25 N/m.
The spring is stretched 0.40 m from its
equilibrium position and released.
• Find the total energy and frequency of
oscillation according to classic calculations
• Assume Planck’s law of energy quantization
applies and find the quantum number n.
• How much energy would be carried way
with one quantum change?
Answers
• 2.0 J, 0.56 Hz, 5.4 * 10^33 = n, change
in energy is 3.7 * 10^-34 J – very small
Another Example
• A mass on a spring is bouncing with the
maximum velocity of 0.25 m/s. The
mass is 0.1 kg and the spring has a
spring constant of 12 N/m. Find the
frequency, total energy, size of one
quantum of energy and n.
Answers
• F = 1.74 Hz,
• KE max = 0.0031 J
• E = hf = 1.15 * 10^-33 J
• Kmax = nhf, n = 2.7 * 10^30
• Huge quantum number
Huge Quantum Numbers
• This is why we don’t normally notice that
energy is quantized
• Because for a given amount of energy,
there are so many quanta of energy
going into it, that it seems continuous to
us
Summary
Apparently, light consists of
tiny bundles of energy called
photons, each having a welldefined quantum of energy.
Planck’s
Equation:
E = hf
Photon
E = hf
(h = 6.626 x 10-34 J s)
The Electron-volt:
1 eV = 1.60 x 10-19 J
1 keV = 1.6 x 10-16 J
1 MeV = 1.6 x 10-13 J