The number of incorrect statement/s about the black body from the following is _________.
(A) Emit or absorb energy in the form of electromagnetic radiation.
(B) Frequency distribution of the emitted radiation depends on temperature.
(C) At a given temperature, intensity vs frequency curve passes through a maximum value.
(D) The maximum of the intensity vs frequency curve is at a higher frequency at higher temperature compared to that at lower temperature.
Detailed Conceptual Analysis
To find the number of incorrect statements, we must evaluate the physical concepts of Black Body Radiation statement by statement.
Evaluating Statement (A):
"Emit or absorb energy in the form of electromagnetic radiation."
✓ CORRECT. By definition, an ideal black body is a perfect absorber and perfect emitter of all frequencies of electromagnetic radiation.
Evaluating Statement (B):
"Frequency distribution of the emitted radiation depends on temperature."
✓ CORRECT. According to Planck's Law and experimentally verified black body curves, the exact distribution of frequencies (and the intensity at each frequency) is solely a function of the absolute temperature (\(T\)) of the black body.
Evaluating Statement (C):
"At a given temperature, intensity vs frequency curve passes through a maximum value."
✓ CORRECT. The spectral intensity curve of a black body does not increase infinitely. It starts at zero, peaks at a specific maximum wavelength/frequency, and then drops back towards zero at the other end of the spectrum.
Evaluating Statement (D):
"The maximum of the intensity vs frequency curve is at a higher frequency at higher temperature compared to that at lower temperature."
✓ CORRECT. This is dictated by Wien's Displacement Law, which states that the maximum wavelength (\(\lambda_{\text{max}}\)) is inversely proportional to temperature:
\( \lambda_{\text{max}} \propto \frac{1}{T} \)
Since frequency (\(\nu\)) and wavelength (\(\lambda\)) are inversely related (\(\nu = \frac{c}{\lambda}\)), it means that frequency is directly proportional to temperature:
\( \nu_{\text{max}} \propto T \)
Therefore, as temperature increases, the peak shifts to a higher frequency (or shorter wavelength).
Conclusion: Since statements A, B, C, and D are all scientifically correct, the number of incorrect statements is exactly 0.
Strengthen Your Theoretical Foundation
In JEE Main and NEET, theoretical questions on Planck's Quantum Theory and Black Body Radiation are designed to test your exact understanding of definitions and graphs. A common error here is misreading "frequency" as "wavelength" in Statement D, leading students to mistakenly mark it as incorrect.
To master the nuances of Wien's Displacement Law, photoelectric effect, and the particle nature of electromagnetic radiation, read our comprehensive notes on the Structure of Atom Class 11 Chemistry.
Continue Your Chemistry Prep
- Access full-length chapter notes, NCERT exemplar solutions, and mock tests for Class XI Chemistry.
- Gearing up for board exams and competitive entrances? Elevate your preparation with our advanced resources for Class XII Chemistry.
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