Contents
Physics Topics are also essential for space exploration, allowing scientists to study phenomena such as gravitational waves and cosmic rays.
What Happens to the Intensity of the Wavelength as the Temperature Increases?
Radiation from a hot body consists of electromagnetic waves of different wavelengths (λ). But the energy is not evenly distributed in all wavelengths of radiation. The intensity of wavelengths in black body radiation, obtained by experimental observations reveals a pattern as shown by the graph in Fig.
The abscissa of the graph denotes the wavelengths λ of radiated heat; and the ordinate denotes radiation per unit area per unit time (Eλ) for different wavelengths.
Interpretation of the graph:
i) At a temperature T1 of the source.
- energy distribution is unequal for different wavelengths and
- the intensity is maximum at a certain wavelength \(\lambda_{m_1}\) as represented by the point P on the graph A.
ii) Radiations from the body at different temperatures T1, T2, T3 and the corresponding intensity distribution can be compared from the graphs A, B, C. Clearly
- as temperature increases the total intensity, represented by the area under the curve, also increases,
- the wavelength of maximum intensity shifts towards the lower wavelength side, with the increase in temperature of the source. The observations referred to above led to the formulation of Wien’s displacement law which can be stated as:
With the increase in the temperature of a body, the wavelength corresponding to the maximum intensity shifts towards the lower wavelength side.
Mathematical representation of Wien’s displacement law is, λmT = b (constant), where λm is the wavelength having maximum intensity at a temperature T of the source. Value of Wien’s constant b, is about 0.0029 m ᐧ K in SI unit. Thus, if λm is known, the temperature of the source T can be calculated. This method is widely used in estimating the temperature of stars. For example, if the temperature of a black body (star) is 100 K,
λm = \(\frac{0.0029}{1000}\) = 2.9 × 10-6m
= 29000 × 10-10m = 29000 Å
This wave lies in the infrared region of electromagnetic spectrum.
Numerical Examples
Example 1.
The wavelength of the radiation of the maximum intensity from the solar surface is 4.9 × 10-7 m. From Wien’s displacement law, find the surface temperature of the sun. [b = 0.0029 m ᐧ K]
Solution:
As per Wien’s displacement law,
λmT = b = 0.0029 m ᐧ K
Hence, T = \(\frac{0.0029}{4.9 \times 10^{-7}}\) = 5918 K.
Example 2.
Assume that a star, which has a surface temperature of 5 × 104K, is a black body. Calculate the wavelength of maximum intensity in its radiation.[b = 0.0029 m ᐧ K]
Solution:
From Wien’s displacement law,
λmT = b ; given, T = 5 × 104K and b = 0.0029 m ᐧ K
∴ λm = \(\frac{b}{T}\) = \(\frac{0.0029}{5 \times 10^4}\) = \(\frac{29}{5}\) × 10-8 = 5.8 × 10-8 m.