The figure below shows the (theoretical) Planck energy distribution for a blackb
ID: 3163499 • Letter: T
Question
The figure below shows the (theoretical) Planck energy distribution for a blackbody radiator at T = 1595K. At what frequency does the maximum energy density occur. For this frequency and temperature calculate the quantities kT and hv and comment on the meaning of these quantities and their values. Calculate the ratio hv/kT and comment on this quantity and value. What is the average oscillator energy predicted by classical theory? What is the average oscillator energy predicted by quantum theory? Calculate the spectral energy density according to classical theory. Calculate the spectral energy predicted by quantum theory.Explanation / Answer
(i) Maximum energy density seems at 1.9 *104 Angstroms.
and Frequency = speed of light/wavelength = 3*108/1.9*10-6= 1.58*1014 Hz.
(ii) h is planck constant and k is boltzmanns constant, so h*v. = 1.58*6.6*10-34+14 = 1.04*10-19 J : is the energy of 1 photon of certain frequency (v).
kT = 1.38*10-23*1595 = 2.20*10-20 J : kT is the amount of total energy(K.E+P.E) of a system according to classical theory.
Classical theory was dependent on temperature and Quantum theory is based on frequency.
(iii) hv/kT = 4.7 approx : So, the energy is not same according to both theories.
(iv) Average total energy as per classical theory is dependent on temperature and is kT, k is boltzmann constant and T is absolute temperature.
(v) Average total energy as per quantum theory is dependent on frequency and is some integral multiple of h*v/2.
Energy cannot be zero in Quantum theory, least amount of energy permitted is called zero point energy and is equal to hv/2 .
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