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. \(0.67~ \text{nm}\)
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?
\(\mathrm{(A)}\) \(\mathrm{(B)}\)
\(\mathrm{(C)}\) \(\mathrm{(D)}\)

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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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.
Choose the correct answer from the options given below:
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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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 \(c=3\times10^{8}~\text{ms}^{-1}\))
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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Given below are two statements:
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.
In the light of the above statements, choose the most appropriate answer from the options given below:
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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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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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)
1. \({e}+2\phi \) 2. \(2{e}-\phi \)
3. \({e}-\phi \) 4. \({e}+\phi \)
Subtopic:  Einstein's Photoelectric Equation |
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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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