Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Bremsstrahlung wikipedia , lookup
Theoretical and experimental justification for the Schrödinger equation wikipedia , lookup
Matter wave wikipedia , lookup
Hawking radiation wikipedia , lookup
Wave–particle duality wikipedia , lookup
X-ray fluorescence wikipedia , lookup
Basic Properties of Stars - 4 §3.4-3.6 Colours of stars and blackbody radiation Colours of stars Stars have colours. Why? Colours of stars Stars have colours. Why? Its not due to their redshift!! Blackbody Radiation Betelgeuse: red Surface Temp = 3600K Rigel: blue-white. Surface Temp = 13,000K Orion Blackbody Radiation History In 1792, Thomas Wedgewood first observed that all his ovens glowed “red-hot” at the same T, regardless of size, shape or materials. All objects T > 0 K emit radiation. Below 800 K in the IR, 800 to 1000 K detected in optical By 3000 K white hot - as T goes up Spectrum shifts to shorter wavelengths & power increases Perfect emitter absorbs all light it receives and reradiates it - called a blackbody. Blackbody Radiation History Perfect blackbody is an idealization, but closely approximated as below. Cavity constant Temp J. Stefan 1879 found Small relation between total hole power emitted and T P=T4 =5.67 x 10-8 W m-2 K-4 Blackbody Radiation Blackbody spectrum depends only on T of source. Blackbody Radiation Blackbody spectrum depends only on T of source. As T increases, max decreases and B()d increases maxT = d (Wien’s Law) and d = 2.898 x 10-3 m K. Blackbody Radiation and Quanta By 1900, Max Planck found empirical formula for blackbody curve. B(T) = (a-5) / e b/T -1 and he tried to derive the constants a and b. Problem is shown on following slides Standing waves Standing waves Blackbody radiation To circumvent this problem, Planck assumed that a standing E-M wave could not acquire any arbitrary amount of energy, but only allowed values that were multiples of a minimum wave energy. This quantum is given by h (or hc/), where h is constant = 6.63 x 10-34 J sec (Planck’s constant). Higher (shorter ) of wave, greater minimum energy. Short , high waves cannot contain even 1 quantum! The Planck Function B(T) = energy emitted per second, per unit wavelength interval d at wavelength , per unit area into a unit solid angle by a blackbody of temperature T (whew!) B(T) = (2hc2/5)(1/ehc/kt - 1) w m-2 m-1 sterad-1 Where c = speed light = 3 x 108 m s-1 k = Boltzmann constant = 1.38 x 10-23 J K-1 h = Planck’s constant = 6.63 x 10-34 J s Only variable in the Planck function is T In terms of frequency B(T) = (2h3/c2)(1/eh/kt - 1) (require Bd =-Bd - as decreases with increasing , d/d = -c/2, B =-B d/d =B c/2) The Planck Function How does Planck function behave in the limits of very high and very low frequency? i.e h/kt >> 1 and << 1 Set h/kT = x B(T) = (2h3/c2)/(ex - 1) For x >> 1, ex -1 = ex so B(T) = (2h3/c2) e-h/kT This called Wien approximation For x << 1, ex = 1 + x + x2/2 + x3/6 + ……… xn/n! = 1 + x Thus B(T) = (2h3/c2)(1/x) = 2kT2/c2 Thus log B(T) = 2 log + log T + constant Blackbody radiation BB radiation - total intensity B(T) = (2h3/c2)(1/eh/kt - 1) The total intensity emitted by the BB is the integral B(T) = B(T)d = B(T)d = (2h3/c2)(1/eh/kt - 1)d where the integral goes from 0 to . Substitute x = h/kT, so that d = (kT/h)dx. Then B(T) = (2hk4T4/c2h4)(x3/ex -1)dx Integral just a real number so that B(T) = AT4 with A = 2k44/15c2h3 So B(T) F T4 (F = T4). This is the Stefan-Boltzmann Law = 5.67 x 10-8 w m-2 K-4 Blackbody Radiation Relation between max and T is known as Wien’s Law maxT= 0.002897755 m K = 0.290 cm K. For a spherical source: F = L / 4R2, (R radius circle surrounding source) from S-B Law F = T4 so L = 4R2Te4 Te is the effective T as stars are not perfect BB radiators T of BB that puts out same energy as the star Blackbody Radiation A simple problem: Lsun = 3.839 x 1026 W and its radius is Rsun = 6.955 x 108 m. (a) What is Te of Sun? (b) Where does Sun’s flux peak? (c) Any relation to the sensitivity of human eye?