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Q. No.Consider a beam of electrons (each electron with energy \(E_0\)) incident on a metal surface kept in an evacuated chamber. Then:
1.
no electrons will be emitted as only photons can emit electrons.
2.
electrons can be emitted but all with energy, \(E_0.\)
3.
electrons can be emitted with any energy, with a maximum of \({E}_0-\phi\) (\(\phi\) is the work function).
4.
electrons can be emitted with any energy, with a maximum \(E_0.\)
Subtopic: Electron Emission |
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A particle moves in a closed orbit around the origin, due to a force which is directed toward the origin. The de-Broglie wavelength of the particle varies cyclically between the two values \(\lambda_{1} , \lambda_{2}\) with \(\lambda_{1} > \lambda_{2}.\) Which of the following statement/s is/are true?
| (a) | The particle could be moving in a circular orbit with the origin as the centre. |
| (b) | The particle could be moving in an elliptic orbit with origin as its focus. |
| (c) | When the de-Broglie wavelength is \(λ_1,\) the particle is nearer the origin than when its value is \(λ_2.\) |
| (d) | When the de-Broglie wavelength is \(λ_2,\) the particle is nearer the origin than when its value is \(λ_1.\) |
Choose the correct option from the given ones:
| 1. | (b) and (d) only |
| 2. | (a) and (c) only |
| 3. | (b), (c), and (d) only |
| 4. | (a), (c), and (d) only |
Subtopic: De-broglie Wavelength |
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Photons absorbed in matter are converted to heat. A source emitting \(n\) photon/sec of frequency \(\nu\) is used to convert \(1~\text{kg}\) of ice at \(0^{\circ}\text{C}\) to water at \(0^{\circ}\text{C}.\) Then, the time \(T\) taken for the conversion:
| (a) | decreases with increasing \(n,\) with \(\nu\) fixed |
| (b) | decreases with \(n\) fixed, \(\nu\) increasing |
| (c) | remains constant with \(n\) and \(\nu\) changing such that \(n\nu=\) constant |
| (d) | increases when the product \(n\nu\) increases |
Choose the correct option:
| 1. | (b), (d) | 2. | (a), (c), (d) |
| 3. | (a), (d) | 4. | (a), (b), (c) |
Subtopic: Particle Nature of Light |
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Relativistic corrections become necessary when the expression for the kinetic energy \(\dfrac{1}{2} mv^{2}\), becomes comparable with \(mc^{2}\), where \(m\) is the mass of the particle. At what de-Broglie wavelength, will relativistic corrections become important for an electron?
| (a) | \(\lambda = 10~\text{nm}\) | (b) | \(\lambda = 10^{-1}~\text{nm}\) |
| (c) | \(\lambda = 10^{- 4}~\text{nm}\) | (d) | \(\lambda = 10^{- 6}~\text{nm}\) |
Choose the correct option:
1. (a), (c)
2. (a), (d)
3. (c), (d)
4. (a), (b)
Subtopic: De-broglie Wavelength |
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The figure shows the stopping potential \(V_0\) (in volts), as a function of frequency \(\nu,\) for a sodium emitter. From the data plotted in the graph, what is the work function of sodium?
(Given: Planck’s constant, \(h=\) \(6.63\times 10^{-34}~\text{J-s}\) and the charge of an electron, \(e=1.6\times 10^{-19}~\text{C}\))
| 1. | \(1.95~\text{eV}\) | 2. | \(2.12~\text{eV}\) |
| 3. | \(1.82~\text{eV}\) | 4. | \(1.66~\text{eV}\) |
Subtopic: Photoelectric Effect: Experiment |
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JEE
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The stopping potential for electrons emitted from a photosensitive surface illuminated with light of wavelength \(491~\text{nm}\) is \(0.710~\text{V}.\) When the wavelength of the incident light changes, the stopping potential increases to \(1.43~\text{V}.\) The new wavelength is approximately:
1. \(329~\text{nm}\)
2. \(309~\text{nm}\)
3. \(382~\text{nm}\)
4. \(400~\text{nm}\)
Subtopic: Einstein's Photoelectric Equation |
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JEE
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A fraction \(f\) of the incident energy in a beam of light of wavelength \(\lambda\) is absorbed by a metallic surface and causes photoemission. If the power of the beam falling on the surface is \(P\), then the maximum photocurrent is:
(\(e\) is electronic charge, \(h\) is Planck's constant, \(c\) is the velocity of light in vacuum)
(\(e\) is electronic charge, \(h\) is Planck's constant, \(c\) is the velocity of light in vacuum)
| 1. | \(\dfrac{\lambda{P}}{h c} f\) | 2. | \(\dfrac{2\lambda{P}}{h c} f\) |
| 3. | \(\dfrac{\lambda{P}}{h c} f e\) | 4. | \(\dfrac{2\lambda{P}}{h c} f e\) |
Subtopic: Photoelectric Effect: Experiment |
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Photons of wavelength \(\lambda\) cause the emission of photoelectrons from a metallic surface, the de-Broglie wavelength of the fastest photoelectron being \(\lambda_d\). A graph of \(\dfrac{1}{\lambda} \text { vs } \dfrac{1}{\lambda_{d}}\) is:
| 1. | a straight line passing through the origin. |
| 2. | a circle. |
| 3. | an ellipse. |
| 4. | a parabola. |
Subtopic: De-broglie Wavelength |
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The electric field associated with a light wave is given by \(E = E_0~ (\sin \omega_1 t)~ (\sin \omega_2 t)\).
This light wave falls on a metal having a threshold frequency, \(\nu_0.\) The maximum kinetic energy of the emitted photoelectrons will be: (\(h\) is Planck's constant)
This light wave falls on a metal having a threshold frequency, \(\nu_0.\) The maximum kinetic energy of the emitted photoelectrons will be: (\(h\) is Planck's constant)
| 1. | Either \(\dfrac{h \omega_{1}}{2 \pi}\) or \(\dfrac{h \omega_{2}}{2 \pi}\) |
| 2. | Either \(\left(\dfrac{h \omega_{1}}{2 \pi}-h \nu_{0}\right)\) or \(\left(\dfrac{h \omega}{2 \pi}-h \nu_{0}\right)\) |
| 3. | \(\dfrac{h\left(\omega_{1}+\omega_{2}\right)}{2 \pi}-h \nu_{0}\) |
| 4. | Both \(\dfrac{h\left(\omega_{1}+\omega_{2}\right)}{2 \pi}-h \nu_{0}\) and \(\dfrac{h\left |\omega_{1}-\omega_{2}\right|}{2 \pi}-h \nu_{0}\) |
Subtopic: Einstein's Photoelectric Equation |
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Photons of frequency \(\nu\) fill a room. A metallic plate having a work function \(W\) \((<h\nu)\) is moved with a velocity \(v\), in this room. The maximum energy of the emitted photoelectrons: (in the plate's frame)
| 1. | does not depend on \(v\) |
| 2. | increases as \(v\) increases |
| 3. | decreases as \(v\) increases |
| 4. | first increases and then decreases as \(v\) is increased |
Subtopic: Einstein's Photoelectric Equation |
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