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: Understanding the Concept:
The Rayleigh-Jeans law is a classical physics approximation to the spectral radiance of electromagnetic radiation from a black body as a function of temperature and frequency. We need to evaluate its successes and failures compared to experimental data.
Step 2: Detailed Explanation:
Let's analyze each statement:

(A) agrees well with experimental results at low frequencies. This is correct. The Rayleigh-Jeans formula matches the experimental black-body radiation curve very well in the low-frequency limit.

(B) agrees well with experimental results at longer wavelengths. This is also correct. Low frequency corresponds to long wavelength (\( c = f\lambda \)). So, this statement is equivalent to statement (A).

(C) shows ultra-violet catastrophe at higher frequencies. This is correct. The law predicts that the radiated energy should increase with the square of the frequency (\( E \propto \nu^2 \)). This implies that as frequency approaches infinity (in the ultraviolet range and beyond), the energy radiated should also become infinite. This contradiction with experimental results, where the energy peaks and then falls off at high frequencies, is famously known as the "ultraviolet catastrophe".

(D) agrees well with experimental results at higher frequencies. This is incorrect. This is precisely where the Rayleigh-Jeans law fails dramatically.
Step 3: Final Answer:
Statements (A), (B), and (C) are correct descriptions of the properties of the Rayleigh-Jeans law. Statement (D) is incorrect. Therefore, the correct combination is (A), (B), and (C).