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 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 = 6.626 x 10-34 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

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 well-defined quantum of energy. E = hf Photon Planck’s Equation: E = hf (h = 6.626 x 10-34 J s) 1 eV = 1.60 x 10-19 J 1 keV = 1.6 x 10-16 J 1 MeV = 1.6 x 10-13 J The Electron-volt: