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Name: Hira
Status: student
Grade: 9-12
Location: N/A
Country: N/A
Date: 5/31/2005


Question:
Hi

Black body temperature curves are luminosity/radiance/intensity graphed against wavelength/frequency. I do not understand how, on these curves, 'this luminosity indicates the NUMBER of photons of radiation rather than the TOTAL ENERGY of the radiation and hence the peaks'. From what I know, the SI units of luminosity is watts, which is TOTAL ENERGY transfer per second. Please could you clarify?


Replies:
To calculate the total power radiated by a given black body at a given temperature, you must add up (integrate) the power radiated in each wavelength (or frequency) interval. The number of photons emitted per second at a given frequency, f, is given by the joules/sec (watts) radiated at that frequency divided by the energy of each photon with that frequency. The energy of a photon of frequency f is given by hf, where h is Planck's constant.

The total energy emitted is not just the energy emitted at the peak frequency, but the sum of the energies emitted at all frequencies.

Best, Dick Plano, Professor of Physics emeritus, Rutgers University


The Planck formula for a "black body" -- that means a body at equilibrium that emits radiation solely as a result of thermal excitation. It may or may not be "black" depending upon the temperature, since the eye only detects electromagnetic radiation between about 400 and 700 nanometers -- can be expressed in terms of temperature, the number of photons, and either the frequency or wavelength of the radiation.

If you go to the web site: http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html and select "blackbody radiation" from the index column on the right hand side of the desktop, you will find the formula expressed in terms of energy, power, and number of photons of a particular frequency or wavelength. The different forms of Planck's formula are just a matter of substituting the relations: frequency x wavelength = c (the speed of light); the energy of a single photon is E = h x frequency (where 'h' is Planck's constant), and the energy of a given frequency (or wavelength) range is the average energy of a photon in that range multiplied by the number of photons in that range.

It is more efficient for you to copy the equations from that source than to try to reproduce them from the limited font selection available in e-mails. In addition, that site is a gold mine of information on many topics in physics, chemistry, and math.

Vince Calder



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