Assertion (A): When ultraviolet light incident on a photo cell, its stopping potential is \(V_S\) and the maximum kinetic energy of photoelectrons is \(K_{\text{max}}\) . When the ultraviolet light is replaced by X-rays, both \(V_S\) and \(K_{\text{max}}\) increases.
Reason (R): Photo electrons are emitted with speed ranging from zero to a maximum value because of the range of frequencies present in the incident 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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Concept: Photoelectric effect and photon energy.
Formula: \(K_{\text{max}} = hf - \phi\) and \(eV_s = K_{\text{max}}\) where \(f\) is frequency.
Solution: X-rays have higher frequency and thus higher photon energy than ultraviolet light. Therefore, incident X-rays will produce photoelectrons with higher maximum kinetic energy (\(K_{\text{max}}\) ) and higher stopping potential (\(V_s\) ). So (A) is true. The range of photoelectron speeds is primarily due to energy losses as electrons travel through the material, not necessarily due to a range of frequencies in the incident light. So (R) is false.
Assertion (A): By de-Broglie hypothesis, \(p = h/\lambda\) for both the electron and the photon.
Reason (R): If an electron has the same wavelength as a photon, they have the same energy.
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: De Broglie wavelength and energy relations.
Formula: De Broglie wavelength \(\lambda = h/p\). Photon energy \(E_p = pc = hc/\lambda\). Electron kinetic energy \(E_e = p^2/(2m) = h^2/(2m\lambda^2)\) (non-relativistic).
Solution: De Broglie's hypothesis states that momentum \(p = h/\lambda\) applies to all particles, including electrons and photons. So (A) is true. If an electron and a photon have the same wavelength, their energies are \(E_p = hc/\lambda\) and \(E_e = h^2/(2m\lambda^2)\), which are generally not equal. So (R) is false.
Assertion (A): Charge of a photon is zero.
Reason (R): 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: Fundamental properties of photons.
Formula: Energy-momentum relation \(E^2 = p^2c^2 + m_0^2c^4\). For a photon, \(m_0 = 0\).
Solution: Photons are the quanta of electromagnetic radiation and do not carry any electric charge. So (A) is true. Photons are massless particles, meaning their rest mass is zero. So (R) is true. The zero rest mass of a photon is intrinsically linked to its inability to carry charge and its nature as a mediator of the electromagnetic force. A charged particle must possess non-zero invariant mass for a consistent description in physics. Therefore, (R) provides a fundamental explanation for (A).
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): 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): In photoelectric effect, on increasing the intensity of light, both the number of electrons emitted and kinetic energy of each of them get increased but photoelectric current remains unchanged.
Reason (R): The photoelectric current depends only on wavelength of 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: Increasing intensity increases number of electrons and current, but KE remains same. Reason (R) is false: Photoelectric current depends on intensity and frequency. 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): Photons do not carry momentum
Reason (R): A photon is a material particle.
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: 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.
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.