Join WhatsApp Icon JEE WhatsApp Group
Question 50

Following figure shows spectrum of an ideal black body at four different temperatures. The number of correct statement/s from the following is _____.

image

A. $$T_4 > T_3 > T_2 > T_1$$
B. The black body consists of particles performing simple harmonic motion.
C. The peak of the spectrum shifts to shorter wavelength as temperature increases.
D. $$\frac{T_1}{\nu_1} = \frac{T_2}{\nu_2} = \frac{T_3}{\nu_3}$$
E. The given spectrum could be explained using quantisation of energy


Correct Answer: 2

Solution

Share
  • Statement A: $$T_4 > T_3 > T_2 > T_1$$  
    Analysis: According to Stefan-Boltzmann law and Wien's displacement law, as the temperature of a black body increases, its peak intensity increases, and the peak wavelength shifts to the left (shorter wavelengths). Looking at the provided graph, the topmost curve represents the highest temperature, meaning $$T_1 > T_2 > T_3 > T_4$$.

    Status: Incorrect

    • Statement B: The black body consists of particles performing simple harmonic motion.
      Analysis: This was a classical mechanics assumption (treating atoms as continuous classical harmonic oscillators), which famously failed to describe the experimental curve, leading to the "ultraviolet catastrophe."

      Status: Incorrect

      • Statement C: The peak of the spectrum shifts to shorter wavelength as temperature increases.
        Analysis: This is the precise statement of Wien’s Displacement Law, which states that the peak wavelength ($$\lambda_{\text{max}}$$) is inversely proportional to the absolute temperature ($$T$$):

        $$\lambda_{\text{max}} \cdot T = \text{constant}$$
        Status: Correct

        • Statement D: $$\frac{T_1}{\nu_1} = \frac{T_2}{\nu_2} = \frac{T_3}{\nu_3} \neq \text{constant}$$
          Analysis: Since $$\nu = \frac{c}{\lambda}$$, Wien’s Displacement Law can be expressed in terms of frequency as $$\frac{\nu_{\text{max}}}{T} = \text{constant}$$. Rearranging this gives $$\frac{T}{\nu_{\text{max}}} = \text{constant}$$. The statement falsely claims that this ratio is not a constant.

          Status: Incorrect

          • Statement E: The given spectrum could be explained using quantisation of energy.
            Analysis: Max Planck successfully explained the complete black-body radiation curve by postulating that energy is emitted or absorbed in discrete packets called quanta ($$E = nh\nu$$).

            Status: Correct

            • The correct statements are C and E.

            Final Answer: 2

              Get AI Help

              Video Solution

              video

              Create a FREE account and get:

              • Free JEE Mains Previous Papers PDF
              • Take JEE Mains paper tests

              Other Cracku’s Useful Resources:

              JEE Questions JEE Question Bank JEE Mains Previous Papers JEE Advanced Previous Papers JEE Study Material PDF JEE Mains Mock Test JEE Advanced Mock Test JEE Daily Target

              Free JEE Questions

              JEE Physics Questions JEE Maths Questions JEE Chemistry Questions
              banner

              banner

              Ask AI