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Q. No.If \(\phi\) is the work function of photosensitive material in electron-volts and light of a wavelength of numerical value \(\lambda=\dfrac{{hc}}{{e}}\) metres is incident on it with energy above its threshold value at an instant, then the maximum kinetic energy of the photo-electron ejected by it at that instant is (in SI units):
(take \(h\) as Plank's constant and \(c\) as the velocity of light in free space)
(take \(h\) as Plank's constant and \(c\) as the velocity of light in free space)
| 1. | \({e}+2\phi \) | 2. | \(2{e}-\phi \) |
| 3. | \({e}-\phi \) | 4. | \({e}+\phi \) |
Subtopic: Einstein's Photoelectric Equation |
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Radiation of wavelength \(280~\text{nm}\) is used in an experiment of photoelectric effect with cathode of work function, \(2.5~\text{eV}.\) The maximum kinetic energy of the photoelectrons is:
(take \(h=6.62\times10^{-34}~\text{J s}\) and \(c=3\times10^{8}~\text{ms}^{-1}\))
(take \(h=6.62\times10^{-34}~\text{J s}\) and \(c=3\times10^{8}~\text{ms}^{-1}\))
| 1. | \(4.4~\text{eV}\) | 2. | \(7.103\times10^{-15}~\text{J}\) |
| 3. | \(1.9~\text{eV}\) | 4. | \(4.60~\text{eV}\) |
Subtopic: Einstein's Photoelectric Equation |
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An electron and an alpha particle are accelerated by the same potential difference. Let \(\lambda_\mathrm{e}\) and \(\lambda_\mathrm{\alpha}\) denote the de-Broglie wavelengths of the electron and the alpha particle, respectively, then:
| 1. | \(\lambda_{\mathrm{e}}>\lambda_{\alpha}\) | 2. | \(\lambda_{\mathrm{e}}=4\lambda_{\alpha}\) |
| 3. | \(\lambda_{\mathrm{e}}=\lambda_{\alpha}\) | 4. | \(\lambda_{\mathrm{e}}<\lambda_{\alpha}\) |
Subtopic: De-broglie Wavelength |
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The work functions of Caesium \((\mathrm{Cs}),\) Potassium \((\mathrm{K}),\) and Sodium \((\mathrm{Na})\) are \(2.14~\text{eV},\) \(2.30~\text{eV}\) and \(2.75~\text{eV}\) respectively. If incident electromagnetic radiation has an incident energy of \(2.20~\text{eV},\) which of these photosensitive surfaces may emit photoelectrons?
| 1. | \(\mathrm{Na}\) only | 2. | \(\mathrm{Cs}\) only |
| 3. | both \(\mathrm{Na}\) and \(\mathrm{K}\) | 4. | \(\mathrm{K}\) only |
Subtopic: Photoelectric Effect: Experiment |
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If \(c\) is the velocity of light in free space, the correct statements about photons among the following are:
| (A) | The energy of a photon is \(E=h\nu.\) |
| (B) | The velocity of a photon is \(c.\) |
| (C) | The momentum of a photon, \(p={\dfrac{h\nu}{c}}.\) |
| (D) | In a photon-electron collision, both total energy and total momentum are conserved. |
| (E) | Photon possesses a positive electric charge. |
| 1. | (A), (B), (C) and (D) only |
| 2. | (A), (C) and (D) only |
| 3. | (A), (B), (D) and (E) only |
| 4. | (A) and (B) only |
Subtopic: Particle Nature of Light |
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The graph that shows the variation of \({\dfrac{1}{\lambda^2}}\) with the kinetic energy \(E\) (where \(\lambda\) is the de-Broglie wavelength of a free particle) is:
| 1. |  |
2. |  |
| 3. |  |
4. |  |
Subtopic: De-broglie Wavelength |
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Which of the following options represents the variation of photoelectric current with the property of light shown on the \(x \text{-}\)axis?
1. \(\mathrm{(A)}\) and \(\mathrm{(D)}\)
2. \(\mathrm{(B)}\) and \(\mathrm{(D)}\)
3. \(\mathrm{(A)}\) only
4. \(\mathrm{(A)}\) and \(\mathrm{(C)}\)
| \(\mathrm{(A)}\) |  |
\(\mathrm{(B)}\) |  |
| \(\mathrm{(C)}\) |  |
\(\mathrm{(D)}\) |  |
1. \(\mathrm{(A)}\) and \(\mathrm{(D)}\)
2. \(\mathrm{(B)}\) and \(\mathrm{(D)}\)
3. \(\mathrm{(A)}\) only
4. \(\mathrm{(A)}\) and \(\mathrm{(C)}\)
Subtopic: Photoelectric Effect: Experiment |
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A photon and an electron (mass \(m\)) have the same energy \(E.\) The ratio \((\lambda_{\text{photon}}/\lambda_{\text{electron}})\) of their de Broglie wavelengths is: (\(c\) is the speed of light)
| 1. | \(c\sqrt{\dfrac{2m}{E}}\) | 2. | \(\dfrac{1}{c}\sqrt{\dfrac{E}{2m}}\) |
| 3. | \(\sqrt{\dfrac{E}{2m}}\) | 4. | \(c\sqrt{2mE}\) |
Subtopic: De-broglie Wavelength |
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Given below are two statements:
In the light of the above statements, choose the most appropriate answer from the options given below:
| Statement I: | The de Broglie wavelength associated with a material particle depends on its charge and nature. |
| Statement II: | The wave nature of particles in sub-atomic domain is significant and measurable. |
| 1. | Both Statement I and Statement II are correct. |
| 2. | Both Statement I and Statement II are incorrect. |
| 3. | Statement I is correct but Statement II is incorrect. |
| 4. | Statement I is incorrect but Statement II is correct. |
Subtopic: De-broglie Wavelength |
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De-Broglie wavelength of an electron orbiting in the \(n=2\) state of hydrogen atom is close to: (Given: Bohr radius \(=0.052~ \text{nm}\))
1. \(1.67~ \text{nm}\)
2. \(2.67~ \text{nm}\)
3. \(0.067~ \text{nm}\)
4. \(0.67~ \text{nm}\)
1. \(1.67~ \text{nm}\)
2. \(2.67~ \text{nm}\)
3. \(0.067~ \text{nm}\)
4. \(0.67~ \text{nm}\)
Subtopic: De-broglie Wavelength |
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