Solved Examples on Wien’s Displacement Law
Example 1: The North star emits energy with a wavelength of 410 nm, while the sun emits light at a maximum intensity of 621 nm. What is the ratio of the surface temperatures of the sun and the north star, if these stars behave like black bodies?
Answer:
According to Wein’s Displacement Law, we know
λmaxT = constant
⇒ T(S) / T(N) = λm(N) / λm(S)
⇒ T(S) / T(N) = 410 / 621
⇒ T(S) / T(N) = 0.66
Example 2: Determine the maximum amount of solar radiation using the assumption that the sun’s surface temperature is 5800 K. Where does this value fall on the electromagnetic spectrum? (b = 2.897 × 10-3 m K).
Answer:
We have,
λmax = b / T
⇒ λmax = 2.897 × 10-3 / 5800
⇒ λmax = 4.995 × 10-7 m
⇒ λmax = 4995 Ă
Example 3: A black body has a wavelength when it is 3510 K in temperature. Its comparable wavelength will be at a temperature of 4100 K.
Answer:
According to Wien’s displacement law, the black body radiation curve peaks for various temperatures at a wavelength that is inversely proportional to the temperature. The typical wavelength is shown to be the wavelength with the highest intensity. i.e.,
λT = constant
⇒ λ × 3510 = λ’ × 4100
⇒ λ’ = 3510 / 4100 λ
⇒ λ’ = 0.85 λ
Example 4: Radiation from stars has a maximal wavelength of 10-5 m. Identify the star’s rough temperature.
Answer:
We have,
λmT = 2.897 × 10-3
⇒ T = 2.897 × 10-3 / 10-5
⇒ T = 2.897 × 102 K
Example 5: Consider that the temperature of the earth is 197 K. Analyze the energy that the planet is emitting at its peak wavelength.
Answer:
We have,
λmT = 2.897 × 10-3
⇒ λm = 2.897 × 10-3 / 197
⇒ λm = 0.014 × 10-3 m
Wien’s Displacement Law
Wein’s Displacement Law or Wein’s Law is named after the man who discovered it, Wilhelm Wien; a German physicist. Wilhelm Wein has done remarkable work in the field of Radiation, for which he was granted a noble price for physics in 1911. Max Planck who was a colleague of Wien, continued his work on the same topic and gave Wein-Plank Law and further a more general law Planck’s Law of Radiation. Wein’s Displacement Law is a fundamental concept in the study of radiation and describes the relationship between the temperature of an object and the wavelength of its maximum emission of radiation. This short article provides a thorough explanation of Wein’s law, including the mathematical formulation and various ways it can be expressed.