 # Wien's Law

Wien’s Law, named after the German Physicist Wilhelm Wien, tells us that objects of different temperatures emit spectra that peak at different wavelengths. Hotter objects emit radiations of shorter wavelength and hence they appear blue. Similarly, cooler objects emit radiations of longer wavelength and hence they appear reddish. In this short piece of article, learn Wein’s law in detail along with the mathematical representation of Wein’s law and other alternative ways to write the formula

## What is Wien’s law?

Wien’s law or Wien’s displacement law, named after Wilhelm Wien was derived in the year 1893 which states that black body radiation has different peaks of temperature at wavelengths that are inversely proportional to temperatures.

Mathematical representation of the law:

$$\begin{array}{l}\lambda _{max} = \frac{b}{T}\end{array}$$

where,
b is the Wien’s displacement constant = 2.8977*103 m.K

T is the temperature in kelvins

### Wien’s constant: b (Wien’s displacement constant)

Physical constant defining the relationship between the thermodynamic temperature of the black body and the wavelength is known as Wien’s constant. It is a product of temperature and wavelength of the black body which grows shorter as the wavelength reaches a maximum with temperature.

### Alternate ways of formula

• Frequency dependent formula:

$$\begin{array}{l}\upsilon _{max} = \frac{\alpha }{h}kT\approx (5.879*10^{10}\frac{Hz}{k})T\end{array}$$

where,
k is the Boltzmann constant
h is the Planck’s constant
T is the temperature in kelvin
𝛼 is the equivalent value = 2.821

• From Planck’s law:

$$\begin{array}{l}\lambda _{max} = \frac{h_{c}}{x}\frac{1}{kT}=\frac{2.8977*10^{6}nm.K}{T}\end{array}$$

### Day-to-day applications

• Incandescent bulb light: With the decrease in temperature of the filament, wavelengths are longer making light appear redder.
• The temperature of the sun: One can study the peak emission per nanometres of the sun with a wavelength of 500 nm in the green spectrum which is in the human eye sensitive range.

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