Dual Nature Of Radiation And Matter

The correct answer is (A): 1.36 eV

Explanation:

- Ø = ΚΕ........(i)
R = = ........(ii)
Putting the values,

Ø ≃ 1.36 eV

Step 1: Formula for de Broglie Wavelength

The de Broglie wavelength ( ) of a particle is given by:

where is Planck's constant and is the momentum of the particle.

Step 2: Momentum and Kinetic Energy

The momentum of a particle is expressed as:

where is the mass of the particle and is its velocity. From the expression for kinetic energy , the velocity can be written as:

• For the proton:
• For the electron:

Step 3: Ratio of de Broglie Wavelengths

The ratio of the de Broglie wavelengths of the proton and the electron is given by:

Substituting the expressions for and :

Simplify the expression:

Step 4: Mass Ratio

Given that the mass of the proton ( ) is 1849 times the mass of the electron ( ), we have:

Final Answer:

The value of is 43, and the ratio of de Broglie wavelengths is .

The correct option is (A): 1:1


Slope = is independent of material
Therefore, the ratio is 1:1.

The correct option is (A): 138 nm

nm

= 138 nm

Solution:
Given:

Therefore, the ratio is . The correct answer is (1).

The correct option is (C)

Statement A: The stopping potential depends only on the work function of the metal.

The stopping potential in the photoelectric effect is given by:

Vs = Kmax / e

where Kmax is the maximum kinetic energy of the emitted electrons and e is the elementary charge. According to Einstein's photoelectric equation:

Kmax = hν - φ

where h is Planck's constant, ν is the frequency of the incident light, and φ is the work function of the metal.

Thus, the stopping potential depends on both the frequency of the incident light and the work function of the metal, not solely on the work function.

Statement A is False.

Statement B: The saturation current increases as the intensity of incident light increases.

The saturation current in the photoelectric effect is directly proportional to the number of incident photons, provided that each photon has enough energy to eject an electron. An increase in the intensity of the incident light means more photons are striking the metal surface per unit time, leading to an increase in the number of photoelectrons emitted, and hence, an increase in the saturation current.

Statement B is True.

Statement C: The maximum kinetic energy of a photoelectron depends on the intensity of the incident light.

From Einstein's photoelectric equation:

Kmax = hν - φ

The maximum kinetic energy depends only on the frequency of the incident light and the work function of the metal. It is independent of the intensity of the incident light, which affects the number of photoelectrons but not their kinetic energy.

Statement C is False.

Statement D: Photoelectric effect can be explained using the wave theory of light.

The wave theory of light fails to explain certain observations of the photoelectric effect, such as the existence of a threshold frequency and the instantaneous emission of electrons regardless of light intensity. These phenomena are successfully explained by the particle theory of light, where light consists of photons with quantized energy.

Statement D is False.

Conclusion: Only Statement B is correct.

The question asks us to identify which phenomenon among the given options is not explained by the wave nature of light. Let's analyze each option to determine this:

1. Reflection: This is a wave phenomenon where light bounces back from a surface. It is explained by the wave nature of light using the laws of reflection.
2. Diffraction: This occurs when light bends around obstacles or through small openings, creating patterns that can only be explained by its wave nature.
3. Photoelectric Effect: This phenomenon involves the emission of electrons from a metal surface when light shines on it. Unlike others, this effect is explained by the particle nature of light (photons), not its wave nature. Thus, this is not explained by the wave nature of light.
4. Interference: This occurs when two or more waves overlap and combine to form new wave patterns. The wave nature of light is essential to explain the interference patterns observed in experiments like the double-slit experiment.
5. Polarization: This phenomenon involves the orientation of oscillations in the light wave and is another clear aspect of the wave nature of light.

From the analysis above, the only phenomenon not explained by the wave nature of light is the photoelectric effect. This observation is key to the development of quantum mechanics where light is described as having both wave and particle properties.

Therefore, the most appropriate answer is: C only.