Assertion (A): The smaller the wavelength of a photon, the more energy it has.
Reason (R): The smaller the wavelength of a photon, the less momentum it has.
Assertion (A) is true: Energy \(E = hc/\lambda\), so smaller \(\lambda\) means more energy. Reason (R) is false: Momentum \(p = h/\lambda\), so smaller \(\lambda\) means more momentum. (A) is true, (R) is false.
Assertion (A): An electron microscope is based on de Broglie’s hypothesis of matter waves.
Reason (R): Higher the accelerating potential, smaller is the de Broglie wavelength of the electron.
Assertion (A) is true: Electron microscopes utilize the wave nature of electrons. Reason (R) is true: de Broglie wavelength \(\lambda = h/\sqrt{2meV}\) decreases with higher potential (V). R explains A, as smaller wavelength allows better resolution.
Assertion (A): Photons do not carry momentum
Reason (R): A photon is a material particle.
Assertion (A) is false: Photons carry momentum \(p = E/c = h/\lambda\). Reason (R) is false: A photon is a quantum of light/energy, not a classical material particle. Both statements are false.
Assertion (A): Increase in intensity of light increases the kinetic energy of photoelectrons.
Reason (R): At stopping potential, no current flows in the circuit.
Assertion (A) is false: Kinetic energy of photoelectrons depends on frequency, not intensity. Reason (R) is true: Stopping potential is the reverse potential that stops all photocurrent. As (A) is false, option (4) is chosen by elimination.
Assertion (A): Kinetic energy of photoelectrons emitted by a photosensitive surface depends upon the intensity of incident photon.
Reason (R): The ejection of electrons from metallic surface is possible with frequency of incident photon below the threshold frequency.
Kinetic energy of photoelectrons depends on the frequency of incident light, not its intensity. Photoelectric emission requires the incident photon's frequency to be above the threshold frequency \(\nu_0\). Thus, both assertion (A) and reason (R) are false.
Assertion (A): Photoelectrons have a range of kinetic energy.
Reason (R): The work function varies as a function of depth from the surface.
Photoelectrons exhibit a range of kinetic energies because electrons lose varying amounts of energy while escaping the material. The work function (\phi\) is a constant for a given surface and does not vary with depth. Thus, assertion (A) is true, but reason (R) is false.
Assertion (A): Photoelectric effect demonstrates the wave nature of light.
Reason (R): The number of photoelectrons is proportional to the frequency of light.
The photoelectric effect experimentally supports the particle (photon) nature of light, not its wave nature. The number of photoelectrons emitted is directly proportional to the intensity of incident light, not its frequency. Therefore, both assertion (A) and reason (R) are false.
Assertion (A): On increasing the frequency of incident light, the photoelectric current increases.
Reason (R): Photoelectric current depends upon the wavelength of incident light.
Increasing the frequency of incident light increases the kinetic energy of emitted photoelectrons, not the photoelectric current. Photoelectric current depends primarily on the intensity of the incident light, provided the frequency is above the threshold. Therefore, both assertion (A) and reason (R) are false.
Assertion (A): In photoelectric effect, the number of photoelectrons emitted is always equal to number of photons incident.
Reason (R): All the photons falling on the surface will eject photoelectrons.
The number of emitted photoelectrons is generally less than the number of incident photons due to quantum efficiency and reflection losses. Photons can only eject electrons if their energy \(\text{h}\nu\) exceeds the work function \(\phi\). Both assertion (A) and reason (R) are false.
Assertion (A): Electron from metal surface ejects only when light of particular wavelength will fall on surface.
Reason (R): Light shows wave nature.
Photoelectric emission occurs only when the incident light's wavelength (\lambda\) is below a specific threshold wavelength (\lambda_0\) (A is true). Light exhibits both wave-like (e.g., diffraction) and particle-like properties (R is true). However, the wave nature of light cannot explain the threshold effect for photoelectric emission. Thus, both A and R are true, but R is not the correct explanation for A.