Luminosity and Frequency
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?
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
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.
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Update: June 2012