Question
Use the formula λm T = 0.29 cm K to obtain the characteristic temperature ranges for different parts of the electromagnetic spectrum. What do the numbers that you obtain tell you?
Solution
We know that, every body at a given temperature T, emits radiations of all wavelengths in a certain range.
For a black body, the wavelength corresponding to maximum intensity of radiation at a given temperature T is given by,
According to Wein's law of radiation
For
In a similar way temperature for other wavelengths can be found.
These numbers tell us the temperature ranges required for obtaining radiations in different parts of the electromagnetic spectrum.
Thus, to obtain visible radiation, say λm = 5 × 10-5 cm, the source should have a temperature
Note: A body at lower temperature will also produce wavelength of this range, but not with maximum intensity.
For a black body, the wavelength corresponding to maximum intensity of radiation at a given temperature T is given by,
According to Wein's law of radiation
For
In a similar way temperature for other wavelengths can be found.
These numbers tell us the temperature ranges required for obtaining radiations in different parts of the electromagnetic spectrum.
Thus, to obtain visible radiation, say λm = 5 × 10-5 cm, the source should have a temperature
Note: A body at lower temperature will also produce wavelength of this range, but not with maximum intensity.
