Derive Planck's Radiation Law
Derive Planck's Radiation Law
Homework Answers
(1) Working with Planck's Law [45 pts] Planck's Law describes the intensity (energy per time per...
(1) Working with Planck's Law [45 pts] Planck's Law describes the intensity (energy per time per area per frequency per angular area) of radiation from a homogeneous, isothermal source: dE 2hc21 Integrating this relation over a spherical hemisphere (outward only) yields the flux density of blackbody radiation from a surface: dE (a) [10 pts] Integrate the above relation over all wavelengths (0 < λ < 00) to derive the total energy flux from a blackbody (the Stefan-Boltzmann Law) dE dtdA...
For blackbody radiation obeying Planck's distribution law show by direct computation that the energy fluctuation for...
For blackbody radiation obeying Planck's distribution law show
by direct computation that the energy fluctuation for radiation in
a volume V in the spectral interval
is given by Einstein's fluctuation formula:
Please show all steps
(u,v + du) ((AE)2) = V (hvu, + envz uz) dv where u,dv is the corresponding energy density. Show that just the first term would result from Wien's distribution law whereas just the second term would result from the Rayleigh-Jeans distribution law.
Use a computer to calculate Planck's radiation law for a temperature of 3000 K, which is...
Use a computer to calculate Planck's radiation law for a temperature of 3000 K, which is the temperature of a typical tungsten filament in an incandescent light bulb. Plot the intensity versus wavelength. (a) How much of the power is in the visible region (400-700nm) compared with the ultraviolet and infrared? (b) What is the ratio of the intensity at 400 nm and 700 nm to the wavelength with maximum intensity?
How Does Planck Derive Wien's Radiation Law?
How Does Planck Derive Wien's Radiation Law?
1.1 Planck's Thermal Radiation Formula (See SQ1) Planck's formula of thermal radiation can be expressed in...
1.1 Planck's Thermal Radiation Formula (See SQ1) Planck's formula of thermal radiation can be expressed in terms of frequency as df (a) From Eq.(1) (right-hand side), work out the units of u(f,T). Hence, state clearly the meaning (b) From Eq(l), show that the Stefan-Boltzmann law follows, i.e, total energy goes like oT and find an expression for the prefactor σ. Hint: The following integral (that you will see in statistical mechanics course) may be useful e-idr = 15 Optional (No...
How did the Energy Quicks enter the image in Planck's emission of Planck's Radiation Act?
How did the Energy Quicks enter the image in Planck's emission of Planck's Radiation Act?
h) What was Planck's intention to deduce Planck's law and how did he do it?
h) What was Planck's intention to deduce Planck's law and how did he do it?
7. What is the relation between temperature and intensity of black body radiation? 8. What is...
7. What is the relation between temperature and intensity of black body radiation? 8. What is the relation between the temperature of a black body and the color of its radiation? 9. What is the closest thing to a black body in our everyday life? 10. What is the importance of Planck's radiation law for modern Physics?
Consider the problem of the distribution of blackbody radiation described in Figure 40.1. Note that as...
Consider the problem of the distribution of blackbody radiation described in Figure 40.1. Note that as T in- creases, the wavelength Amax at which I(?, T) reaches a maximum shifts toward shorter wavelengths. (a) Show that there is a general relationship between tempera- ture and ?max (known as Wien's displacement law which states that Txconstant. (b) Obtain a nu- merical value for this constant. [Hint: Start with Planck's radiation law and note that the slope of1(2, T) versus ? is...
28. Planck's constant h arose in his research on A. angular momentum. B. temperatures and "blackbody"...
28. Planck's constant h arose in his research on A. angular momentum. B. temperatures and "blackbody" radiation. C. donuts. D. crystallographic density 26. The spring constant, k, in the spring force law, F = -kx, is A. the ratio of gravitational and electromagnetic interactions at the atomic scale. B. the northern hemisphere value of Coulomb’s constant. C. the potential energy of a spring at equilibrium position. D. a property of a spring that encodes the spring’s stiffness against compression or...
(1) Working with Planck's Law [45 pts] Planck's Law describes the intensity (energy per time per area per frequency per angular area) of radiation from a homogeneous, isothermal source: dE 2hc21 Integrating this relation over a spherical hemisphere (outward only) yields the flux density of blackbody radiation from a surface: dE (a) [10 pts] Integrate the above relation over all wavelengths (0 < λ < 00) to derive the total energy flux from a blackbody (the Stefan-Boltzmann Law) dE dtdA...
For blackbody radiation obeying Planck's distribution law show
by direct computation that the energy fluctuation for radiation in
a volume V in the spectral interval
is given by Einstein's fluctuation formula:
Please show all steps
(u,v + du) ((AE)2) = V (hvu, + envz uz) dv where u,dv is the corresponding energy density. Show that just the first term would result from Wien's distribution law whereas just the second term would result from the Rayleigh-Jeans distribution law.
1.1 Planck's Thermal Radiation Formula (See SQ1) Planck's formula of thermal radiation can be expressed in terms of frequency as df (a) From Eq.(1) (right-hand side), work out the units of u(f,T). Hence, state clearly the meaning (b) From Eq(l), show that the Stefan-Boltzmann law follows, i.e, total energy goes like oT and find an expression for the prefactor σ. Hint: The following integral (that you will see in statistical mechanics course) may be useful e-idr = 15 Optional (No...
7. What is the relation between temperature and intensity of black body radiation? 8. What is the relation between the temperature of a black body and the color of its radiation? 9. What is the closest thing to a black body in our everyday life? 10. What is the importance of Planck's radiation law for modern Physics?
Consider the problem of the distribution of blackbody radiation described in Figure 40.1. Note that as T in- creases, the wavelength Amax at which I(?, T) reaches a maximum shifts toward shorter wavelengths. (a) Show that there is a general relationship between tempera- ture and ?max (known as Wien's displacement law which states that Txconstant. (b) Obtain a nu- merical value for this constant. [Hint: Start with Planck's radiation law and note that the slope of1(2, T) versus ? is...
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