Question

Observe the following statements
Statement-I: Rutherford model of an atom cannot explain the stability of an atom
Statement-II: The wavelength of X-rays is higher than the wavelength of microwaves
The correct answer is

• A. Both statements I and II are correct
• B. Both statements I and II are not correct
• C. Statement I is correct, but statement II is not correct
• D. Statement I is not correct, but statement II is correct

Hint:

The instability of the Rutherford atom is a classic failure point of the model due to classical electrodynamics. Always remember the order of the electromagnetic spectrum: X-rays have high energy/frequency and short wavelength, while Microwaves have low energy/frequency and long wavelength.

Answer 1

The Correct Option is C

Step 1: Analyze Statement-I (Rutherford Model and Stability).
The Rutherford model (the planetary model) proposes that electrons revolve around a positively charged nucleus.
According to classical electromagnetic theory (Maxwell's equations), an accelerating charged particle (like an electron in orbit) must continuously radiate energy.
The continuous radiation of energy would cause the electron's orbit to shrink rapidly, eventually spiraling into the nucleus.
This process would take about $10^{-8}$ seconds, meaning the atom would be highly unstable. The Rutherford model offers no explanation for this inherent instability.
Therefore, Statement-I is correct.

Step 2: Analyze Statement-II (Wavelength of X-rays and Microwaves).
Electromagnetic waves are ordered by their frequency ($\nu$) and wavelength ($\lambda$) in the electromagnetic spectrum. The relation is $\lambda = c/\nu$.
The order of increasing wavelength (decreasing frequency) is: Gamma rays<X-rays<Ultraviolet<Visible<Infrared<Microwaves<Radio waves.
Microwaves have a much longer wavelength than X-rays. $\lambda_{\text{X-rays}} \approx 0.01 \text{ nm}$ to $10 \text{ nm}$, while $\lambda_{\text{Microwaves}} \approx 1 \text{ mm}$ to $1 \text{ m}$.
The statement claims $\lambda_{\text{X-rays}}>\lambda_{\text{Microwaves}}$, which is false.
Therefore, Statement-II is not correct.

Step 3: Conclude the correct option.
Statement I is correct, but Statement II is not correct.