Physics · Thermal Properties Of Matter · NEET
It DECREASES. Since lambda_m times T = b (constant), T and lambda_m are inversely proportional. When T goes up, lambda_m goes down. The peak of the radiation curve shifts to shorter wavelength (toward blue/UV). That is why the law is called a 'displacement' law: the peak is displaced to a shorter wavelength as temperature rises.
b = 2.9 x 10^-3 metre kelvin (m K), often written 2.898 x 10^-3 m K. In the formula lambda_m times T = b, lambda_m is in metres and T is in kelvin. If you want lambda_m in nanometres, use b = 2.9 x 10^6 nm K. Always keep units consistent.
A star behaves like a black body. A hot star (say 10000 K) has a small lambda_m that falls in the blue part of the spectrum, so it looks bluish. A cool star (say 3000 K) has a larger lambda_m in the red part, so it looks reddish. Same law: higher T pushes the peak to shorter (bluer) wavelength.
Always Kelvin (absolute temperature). Wien's law comes from black-body physics which uses absolute temperature. If a problem gives Celsius, convert first: T(K) = T(C) + 273. Using Celsius gives a wrong lambda_m.
Wien's law tells you WHERE the peak of the radiation is (which wavelength carries the most energy): lambda_m times T = b. Stefan-Boltzmann law tells you HOW MUCH total energy the body radiates: E is proportional to T^4. One is about colour/wavelength, the other is about total power.
Try the real previous-year questions from this chapter — each with the answer and a full solution.
The wavelength of maximum energy radiation (lambda_m) from a black body is inversely proportional to its absolute temperature: lambda_m times T = b, a constant.
lambda_m = b / T = 2.9 x 10^-3 / 5800 = 5.0 x 10^-7 m = 500 nm, which is green-yellow visible light. That is why sunlight peaks in the visible band.
Peak wavelength becomes half. Since lambda_m is inversely proportional to T, doubling T halves lambda_m. The radiation shifts to shorter, bluer wavelengths.
It is exact for an ideal black body, but real hot objects (stars, filaments, glowing iron) follow it closely enough to estimate their temperature from the colour of their peak radiation.
Measure the wavelength lambda_m at which the body radiates most strongly, then compute T = b / lambda_m. This is how astronomers find star temperatures from their colour.
