Question

The Rayleigh Jean's Law,
(A) agrees well with experimental results at low frequencies.
(B) agrees well with experimental results at longer. wavelengths.
(C) shows ultra-violet catastrophe at higher frequencies.
(D) agrees well with experimental results at higher frequencies.
Choose the correct answer from the options given below:

• A. (A), (B) and (D) only
• B. (A), (B) and (C) only
• C. (B), (C) and (D) only
• D. (A), (C) and (D) only

Hint:

Remember the key features of the black-body radiation laws:
{Rayleigh-Jeans Law:} Classical, works for low frequencies/long wavelengths, fails at high frequencies (ultraviolet catastrophe).
{Wien's Law:} Early quantum theory, works for high frequencies/short wavelengths, fails at low frequencies.
{Planck's Law:} Full quantum theory, works perfectly across all frequencies.

Answer 1

The Correct Option is B

Step 1: Concept Overview:
The Rayleigh-Jeans law is a classical physics approximation for the spectral radiance of electromagnetic radiation from a black body, dependent on temperature and frequency. Its validity needs to be assessed against experimental data, noting its successes and limitations.
Step 2: Statement Analysis:
Evaluate each statement:

(A) Agreement at Low Frequencies: Correct. The Rayleigh-Jeans formula accurately approximates experimental black-body radiation curves at low frequencies.

(B) Agreement at Long Wavelengths: Correct. Low frequency corresponds to long wavelengths (\( c = f\lambda \)), making this statement equivalent to (A).

(C) Ultraviolet Catastrophe at High Frequencies: Correct. The law predicts energy increase with the square of frequency (\( E \propto u^2 \)), implying infinite radiated energy at infinite frequency (ultraviolet and beyond). This contradicts experimental observations, where energy peaks and then declines, a phenomenon known as the "ultraviolet catastrophe".

(D) Agreement at High Frequencies: Incorrect. This is where the Rayleigh-Jeans law fails significantly.
Step 3: Conclusion:
Statements (A), (B), and (C) accurately describe the Rayleigh-Jeans law. Statement (D) is inaccurate. Therefore, the correct statements are (A), (B), and (C).