Ncert Exercises & Solutions

8.13 Use the formula $λ_{m} T = 0.29 cm -K$ to obtain the characteristic temperature ranges for different parts of the electromagnetic spectrum. What do the numbers that you obtain tell you?

Hint: A body at a perticular temperature produces a continuous spectrum of wavelength.

Step 1: Find the temperature for different wavelengths.
Planck’s law gives the wavelength corresponding to the maximum intensity of radiation. Planck's law is written as:

$λ_{m} T = 0.29 cm K$

The temperature for different wavelengths are given as:

$For λ_{m} = 10^{- 4} cm; T = \frac{0.29}{10^{- 4}} = 2900 ° K$
$For λ_{m} = 5 \times 10^{- 5} cm; T = \frac{0.29}{5 \times 10^{- 5}} = 5800 ° K$
$For λ_{m} = 10^{- 6} cm; T = \frac{0.29}{10^{- 6}} = 290000 ° K$ The numbers obtained show that the bodies emit different wavelengths at different temperatures.

Step 2: Find the relation between wavelength and temperature.
As the wavelength decreases, the corresponding temperature increases.

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