Use the formula λ_mT = 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?

According to the planck’s law of radiation:

λ_m T = 0.29 cm K

or λ_m = 0.29/T cm K

where T is the temperature and λ_m is the maximum wavelength of the wave

for different values of maximum wavelengths such as λ_m = 10^-4 cm, 5 × 10^-5 cm and 10^-6 cm, the values for temperatures can be calculated as follows:

T = 0.29/λ_m cm K

When, λ_m = 10^-4 cm

T = 0.29/10^-4 cm K

T = 2900 K

When, λ_m = 5× 10^-5 cm

T = cm K

T = 5800 K

When, λ_m = 10^-6 cm

T = 0.29/10^-6 cm K

T = 290000 K

The above data shows that temperature is required to get radiations of different parts of electromagnetic spectrum and the temperature increases with decrease in the wavelength.