3. Plan for Today (AP Physics 2)
Questions on HW (due tomorrow)
Notes/Lecture on Blackbody Radiation

4. 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

5. 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

6. 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

7. 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

8. See how there’s less and less light

9. 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!

10. Intensity vs. Frequency and Catastrophe

11. Intensity vs. Wavelength

12. 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

14. Wien’s Displacement Law

15. Wien’s Displacement
Max Wavelength * T = * 10^-2 m*K

16. 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

17. Planck Came up with the idea that energy can’t be arbitrary values
Instead, energy is quantized

18. Plank’s Constant E = nhf (h = 6.626 x 10-34 J s)
In his studies of black-body radiation, Maxwell Planck discovered that electromagnetic energy is emitted or absorbed in discrete quantities.
Planck’s Equation:
E = nhf (h = x J s)
n is positive integer, f is frequency
Apparently, light consists of tiny bundles of energy called photons, each having a well-defined quantum of energy.
E = hf
Photon

19. Link to more information

20. Blackbody Spectrum
PHET

21. 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”

22. Example Problem
Temperature of the skin is about 35 degrees Celsius. At what wavelength does the radiation emitted from the skin reach its peak?

23. Answer
940 micrometers

24. 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?

25. Answers
2.0 J, 0.56 Hz, 5.4 * 10^33 = n, change in energy is 3.7 * 10^-34 J – very small

26. 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.

27. 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

28. 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

29. Summary
Apparently, light consists of tiny bundles of energy called photons, each having a well-defined quantum of energy.
E = hf
Photon
Planck’s Equation:
E = hf (h = x J s)
1 eV = 1.60 x J
1 keV = 1.6 x J
1 MeV = 1.6 x J
The Electron-volt: