Question

Use the formula lmT = 0.29 cmK to obtain the characteristictemperature ranges for different parts of the electromagneticspectrum. What do the numbers that you obtain tell you?

Answer 1

The relation between temperature and wavelength is given as,

λ m T=0.29 cmK

Where, λ m is the wavelength and T is the temperature for wavelength.

By substituting the values for λ m = 10 −4  cm in the above expression, we get

( 10 −4  cm ) T 1 =0.29 cmK T 1 = 0.29 cmK 10 −4  cm =2900 K

By substituting the values for λ m =5× 10 −5  cm in the above expression, we get

T 2 = 0.29 cmK 5× 10 −5  cm =5800 K

By substituting the values for λ m = 10 −6  cm in the above expression, we get

T 3 = 0.29 cmK 10 −6  cm =290000 K

And so on.

The numbers obtained from the above calculations shows that as the wavelength decrease, the corresponding temperature increases, this implies that the wavelength is inversely proportional to the temperature. Hence, the numbers obtained shows us that the suitable temperature ranges are required to obtain radiations of suitable wavelength.