Modern Physics

Step 1: Understanding the Concept:
This problem describes Compton scattering, an effect where X-rays or gamma rays scatter off charged particles (usually electrons), resulting in an increase in the wavelength of the scattered radiation. The change in wavelength depends on the scattering angle.
Step 2: Key Formula or Approach:
The Compton scattering formula gives the change in wavelength :
where is the scattered wavelength, is the incident wavelength, is the Compton wavelength of the electron ( ), and is the scattering angle.
Step 3: Detailed Explanation:
1. Identify the given values:
Incident wavelength, pm.
Compton wavelength, pm.
Scattering angle, .
2. Calculate the change in wavelength ( ):
First, find the cosine of the scattering angle: .
Now, substitute the values into the Compton formula:
3. Calculate the scattered wavelength ( ):
The new wavelength is the original wavelength plus the change.
Step 4: Final Answer:
The wavelength of the X-rays scattered through 60° is 16.213 pm.

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 ( ). 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 ( ). 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).

Step 1: Understanding the Concept:
The photoelectric effect is the emission of electrons when light shines on a material. This question tests the key experimental observations and their explanations based on the quantum (photon) model of light.
Step 2: Detailed Explanation:
Let's evaluate each statement:

(A) There is no time interval... This is a correct and crucial observation. The emission is practically instantaneous, which contradicts the classical wave theory of light that predicted a significant time lag for energy to accumulate.

(B) Higher the frequency of light, more is the kinetic energy... This is correct. Einstein's photoelectric equation is , where is the frequency. This shows a linear relationship between the maximum kinetic energy of photoelectrons and the frequency of the incident light (above the threshold frequency).

(C) A bright light yields more photo-electrons... This is correct. The brightness (intensity) of light is proportional to the number of photons incident per unit time. A higher intensity means more photons are available to interact with electrons, leading to the emission of more photoelectrons (a higher photocurrent).

(D) Blue light emits slower electrons than red light. This is incorrect. Blue light has a higher frequency than red light. According to Einstein's equation, the higher frequency of blue light will result in photoelectrons with *higher* maximum kinetic energy (and thus higher speeds) compared to those emitted by red light (assuming both frequencies are above the threshold).
Step 3: Final Answer:
Statements (A), (B), and (C) are correct descriptions of the photoelectric effect. Statement (D) is incorrect. Thus, the correct option is (A).

Concept: Wien's displacement law relates the temperature of a black body to the wavelength at which it emits maximum radiation.
Step 1: Wien's law formula.
where is Wien's constant.
Step 2: Rewriting the relation.

Step 3: Understanding the relationship.
As temperature increases, the peak wavelength decreases.
Step 4: Evaluating the options.

• Incorrect
• Correct
• Incorrect
• Incorrect

Step 5: Conclusion.
Thus, is inversely proportional to temperature.

Concept: Compton shift refers to the change in wavelength of a photon when it is scattered by a particle such as an electron.
Step 1: Compton shift formula.

Step 2: Given condition.
For backscattering,
Step 3: Substitute the value.

Step 4: Evaluating the options.

• Incorrect
• Correct
• Incorrect
• Incorrect

Step 5: Conclusion.
Thus, the Compton shift for backscattering is .

Concept: Newton's rings are formed due to interference of light waves reflected from the top and bottom surfaces of a thin air film formed between a plano-convex lens and a glass plate.
Step 1: Formation of air film.
When a plano-convex lens is placed on a flat glass plate, a thin layer of air is trapped between them.
Step 2: Nature of the air film.
The thickness of this air film gradually increases from the point of contact outward.
Step 3: Shape identification.
Since the thickness varies continuously in one direction, the air film behaves like a wedge-shaped film.
Step 4: Evaluating the options.

• Plane Uniform thickness (incorrect)
• Cylindrical Not applicable (incorrect)
• Spherical Lens is spherical, but film is not (incorrect)
• Wedge-shaped Thickness varies gradually (correct)

Step 5: Additional insight.
The varying thickness of the air film causes constructive and destructive interference, producing concentric circular fringes known as Newton's rings.
Step 6: Conclusion.
Thus, the air film formed in Newton's rings experiment is wedge-shaped.