Assertion (A): The relative velocity of two photons travelling in opposite directions is \(c\).
Reason (R): The rest mass of a photon is zero.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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Concept: Special Relativity, velocity addition formula.
Formula: Relativistic velocity addition \(v_{\text{rel}} = \frac{v_1 - v_2}{1 - \frac{v_1 v_2}{c^2}}\) where \(v_1, v_2\) are velocities of two objects.
Solution: For two photons moving in opposite directions (\(v_1 = c, v_2 = -c\)), the relativistic velocity addition formula gives \(v_{\text{rel}} = \frac{c - (-c)}{1 - \frac{c(-c)}{c^2}} = \frac{2c}{1+1} = c\). So (A) is true. The rest mass of a photon is zero, which is the reason why photons always travel at the speed of light \(c\) in all inertial frames, forming the foundation of special relativity. Thus, (R) explains the relativistic behavior described in (A).
Assertion (A): Increase in intensity of light increases the kinetic energy of photoelectrons.
Reason (R): At stopping potential, no current flows in the circuit.
1. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (3) (A) is true but (R) is false
4. (4) Both (A) and (R) are false
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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): Work function of a metal increases with increase in intensity of incident light.
Reason (R): Maximum kinetic energy of ejected photoelectrons depends upon the intensity of incident light.
1. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (3) (A) is true but (R) is false
4. (4) Both (A) and (R) are false
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Assertion (A) is false: Work function is a characteristic property of the metal and is independent of light intensity.
Reason (R) is false: Maximum kinetic energy depends on frequency, not intensity. Both statements are false.
Assertion (A): In the process of photo electric emission, all the emitted photoelectrons have same KE.
Reason (R): According to Einstein’s photo electric equation \(KE= h\nu – \phi\).
1. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (3) (A) is true but (R) is false
4. (4) Both (A) and (R) are false
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Assertion (A) is false: Kinetic energy of emitted photoelectrons varies from zero to maximum. Reason (R) is false: Einstein's equation is \(KE_{max}= h\nu - \phi\). Both statements are false.
Assertion (A): In photo electric effect, photo electrons come out from inner orbits of atom.
Reason (R): Free electrons of the metal can not absorb energy of a photon.
1. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (3) (A) is true but (R) is false
4. (4) Both (A) and (R) are false
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Assertion (A) is false: Photoelectrons are ejected from the surface of the metal, not inner orbits. Reason (R) is false: Free electrons absorb photon energy to be ejected. Both statements are false.
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.
1. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (3) (A) is true but (R) is false
4. (4) Both (A) and (R) are false
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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.
1. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (3) (A) is true but (R) is false
4. (4) Both (A) and (R) are false
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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): 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.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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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.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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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.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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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.