Question

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

[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 wavelengths as temperature increases.
[D.] \(\frac{T_1}{\nu_1} = \frac{T_2}{\nu_2} = \frac{T_3}{\nu_3} \neq \text{constant}.\)
[E.] The given spectrum could be explained using quantization of energy.

Hint:

Wien’s Displacement Law:} \(\lambda_{\text{max}} \propto \frac{1}{T}\).
Blackbody radiation follows Planck’s quantization of energy: \(E = h\nu\).

Answer 1

Correct Answer: 2

The given spectrum of an ideal black body at different temperatures can be analyzed using Wien's Displacement Law and concepts of black body radiation. Let's evaluate the statements provided:

[A.] \(T_4 > T_3 > T_2 > T_1\)
According to Wien's Displacement Law, the peak wavelength \(\lambda_{\text{max}}\) decreases as the temperature increases. Hence, if the peak shifts to shorter wavelengths, the temperature order will be \(T_4 > T_3 > T_2 > T_1\). This statement is correct.

[B.] The black body consists of particles performing simple harmonic motion.
This is incorrect. Black body radiation concerns electromagnetic radiation emissions, not the physical motion of particles.

[C.] The peak of the spectrum shifts to shorter wavelengths as temperature increases.
From Wien's Displacement Law, higher temperatures correlate with shorter peak wavelengths. Thus, this statement is correct.

[D.] \(\frac{T_1}{\nu_1} = \frac{T_2}{\nu_2} = \frac{T_3}{\nu_3} \neq \text{constant}.\)
Wien's Law states \(\lambda_{\text{max}}T = \text{constant}\), meaning \(\nu \propto T\). Hence, \(\frac{T}{\nu}\) is not a constant. This statement is qualitatively aligned with black body radiation, thus correct.

[E.] The given spectrum could be explained using quantization of energy.
This statement is true as black body radiation can be explained by quantization, as shown by Planck's Law.