A metallic ball (work function: \(2\) eV) is irradiated with light consisting of photons of wavelength \(200\) nm. The ball has an initial charge, giving it a potential \(1\) V. Take the product of Planck's constant and velocity of light, hc as \(1240\) eV-nm. The final potential of the ball, when photoemission practically stops, is: 
1. \(2\)
2. \(3.2\)
3. \(4.2\)
4. \(5.2\) V

Subtopic:  Photoelectric Effect: Experiment |
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Photoelectrons emerging from a photocathode (work function: \(2.2~\text{eV}\)) are allowed to fall onto a gas containing hydrogen atoms in the ground state and the first excited state. What is the minimum energy of the photons incident on the photo-cathode that will cause the photoelectrons to transfer energy to the \(\mathrm{H\text-}\)atoms?
1. \(13.6~\text{eV}+2.2~\text{eV}\)
2. \((10.2+2.2)~\text{eV}\)
3. \((3.4+2.2)~\text{eV}\)
4. \((1.89+2.2)~\text{eV}\)
Subtopic:  Photoelectric Effect: Experiment |
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A photon of energy \(E_p\) has the same wavelength as an electron of kinetic energy \(E_e.\) The rest energy (i.e., \(mc^2\)) of the electron is:
1. \(\dfrac{E^2_p}{E_e}\)

2. \(\dfrac{E^2_e}{E_p}\)

3. \(\dfrac{E^2_e}{2E_p}\)

4. \(\dfrac{E^2_p}{2E_e}\)
Subtopic:  De-broglie Wavelength |
 67%
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Ultraviolet photons, each of energy \(20~\text{eV},\) are incident onto a gas of \(\mathrm {H}\)-atoms, causing the emission of electrons. The kinetic energy of the emitted electrons has the value:
1. \(6.4~\text{eV}\)
2. \(7.2~\text{eV}\)
3. \(3.2~\text{eV}\)
4. \(13.6~\text{eV}\)
Subtopic:  Electron Emission |
 68%
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Photons of light of wavelength, \(\lambda=400\) nm are incident on a composite photocathode consisting of multiple regions with metals having work functions of \(2.1\) eV and \(1.1\) eV. The emitted photoelectrons are sent through a retarding potential difference, \(V_0\). What is the minimum value of \(V_0\) required to stop all electrons? (take: \(hc=1240\) eV-nm)
1. \(1\) V 2. \(1.5\) V
3. \(2\) V 4. \(5.2\) V
Subtopic:  Einstein's Photoelectric Equation |
 52%
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The de-Broglie wavelength of the electron accelerated through a potential difference \(V\) equals the de-Broglie wavelength of an electron in the ground state of the hydrogen atom. The value of \(V\) is:
1. \(13.6\) volts
2. \(27.2\) volts
3. \(10.2\) volts
4. \(6.8\) volts
Subtopic:  De-broglie Wavelength |
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The de-Broglie wavelength of a photon of energy \(E\) is \(\lambda_{ph}\) and that of an electron (non-relativistic) of the same energy \(E\) is \(\lambda_{e}.\) Then (assume \(E\text ~\)few \(e\text{V}\)):
1. \(\lambda_{ph}=\lambda_e\)
2. \(\lambda_{ph}<\lambda_e\)
3. \(\lambda_{ph}>\lambda_e\)
4. any of the above may be true
Subtopic:  De-broglie Wavelength |
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A hydrogen atom \((\mathrm{H})\) and a helium \((\mathrm{He})\) atom, both have the same kinetic energy (they are non-relativistic). Their de-Broglie wavelengths are in the ratio: \(\Large\frac{\lambda_\mathrm{H}}{\lambda_{\mathrm{He}}}=\)
1. \(4\) 2. \(\dfrac14\)
3. \(2\) 4. \(\dfrac12\)
Subtopic:  De-broglie Wavelength |
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The frequency of light in a photoelectric experiment is tripled. The stopping potential will:
1. be tripled 2. be more than tripled
3. be less than tripled 4. become one-third
Subtopic:  Photoelectric Effect: Experiment |
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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 |
 56%
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