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Q. No.The electric field associated with a light beam incident on a metallic surface with work-function \(3.0\) eV, is given by; \(E = E_o~\sin (\pi \times 10^7 \text{m}^{-1}) (x-ct)\). The stopping potential for the emitted photoelectrons is: (take \(hc=1240\) eV-nm, if required)
1.
\(0.1\)
2.
\(3.2\)
3.
\(9.4\)
4.
none of the above
Subtopic: Â Einstein's Photoelectric Equation |
 76%
Level 2: 60%+
Hints
Photons of energy \(h\nu\) (\(\nu=\) frequency) incident onto a photocathode cause the emission of photoelectrons, and a current flows in the circuit. Assume the photoelectrons are emitted normal to the photocathode. A uniform magnetic field \(B\) is switched on parallel to the plates (into the plane). The work function is \(W\) and the separation between the cathode and anode is \(d.\) The minimum value of \(B\) for which the ammeter shows zero current satisfies:
(where \(m\) is the mass of the electron and \(e\) is the charge of the electron)
1. \(Bed=(h\nu-W)\)
2. \((Bed)^2=m(h\nu+W)\)
3. \((Bed)^2=2m(h\nu-W)\)
4. \((Bed)^2=2m(h\nu+W)\)
(where \(m\) is the mass of the electron and \(e\) is the charge of the electron)
1. \(Bed=(h\nu-W)\)
2. \((Bed)^2=m(h\nu+W)\)
3. \((Bed)^2=2m(h\nu-W)\)
4. \((Bed)^2=2m(h\nu+W)\)
Subtopic: Â Einstein's Photoelectric Equation |
 64%
Level 2: 60%+
Hints
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: Â Einstein's Photoelectric Equation |
 57%
Level 3: 35%-60%
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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: Â Photoelectric Effect: Experiment |
 54%
Level 3: 35%-60%
Hints
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: Â Einstein's Photoelectric Equation |
 53%
Level 3: 35%-60%
Hints
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. \(2\) V
2. \(3.2\) V
3. \(4.2\) V
4. \(5.2\) V
1. \(2\) V
2. \(3.2\) V
3. \(4.2\) V
4. \(5.2\) V
Subtopic: Â Photoelectric Effect: Experiment |
 53%
Level 3: 35%-60%
Hints
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: Â Photoelectric Effect: Experiment |
Level 4: Below 35%
Hints
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: Â Einstein's Photoelectric Equation |
Level 3: 35%-60%
Hints
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: Â De-broglie Wavelength |
Level 3: 35%-60%
Hints
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: Â Photoelectric Effect: Experiment |
 57%
Level 3: 35%-60%
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