Blackbody Radiation Wavelength – Rankers Physics
Topic: Thermal Physics
Subtopic: Heat Transfer - Radiation

Blackbody Radiation Wavelength

Assertion (A): As the temperature of the blackbody increases, the wavelength at which the spectral intensity \(E_\lambda\) is maximum decreases.
Reason (R): The wavelength at which the spectral intensity will be maximum for a black body is proportional to the fourth power of its absolute temperature.
 
(1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
(2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
(3) (A) is true but (R) is false
(4) Both (A) and (R) are false

Solution:

Assertion (A) is true according to Wien's displacement law, \(\lambda_{max} T = \text{constant}\). Reason (R) is false as \(\lambda_{max}\) is inversely proportional to temperature, not proportional to \(T^4\). \(E = \sigma T^4\) relates total emissive power to temperature.

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