Q. No.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.
\(\dfrac12\)
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| 1. | a straight line with a positive intercept on the \(x\)-axis (frequency) |
| 2. | a straight line with a positive intercept on the \(y\)-axis (kinetic energy) |
| 3. | a parabola |
| 4. | a hyperbola |
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| 1. |  |
2. |  |
| 3. |  |
4. |  |
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| Statement I: | By de-Broglie's hypothesis momentum of an electron, \(p=h/ \lambda\). |
| Statement II: | The energy of an electron is given by; \(E=hc/ \lambda\). |
| 1. | Statement I is correct and Statement II is incorrect. |
| 2. | Statement I is incorrect and Statement II is correct. |
| 3. | Both Statement I and Statement II are correct. |
| 4. | Both Statement I and Statement II are incorrect. |
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| 1. | photon |
| 2. | electron |
| 3. | neither, since both have equal momenta |
| 4. | it could be either, depending on the energy |
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1. \(4\)
2. \(2\)
3. \(\dfrac12\)
4. \(\dfrac14\)
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(Take \(hc=12400\) eV-\(\mathring A\))
1. \(0.5\) eV
2. \(3.1\) eV
3. \(1.1\) eV
4. \(2\) eV
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1. \(\lambda_{ph}=\lambda_e\)
2. \(\lambda_{ph}<\lambda_e\)
3. \(\lambda_{ph}>\lambda_e\)
4. any of the above may be true
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| Column-I | Column-II | ||
| \(\mathrm{(A)}\) | Radiation pressure | \(\mathrm{(I)}\) | Particle nature of radiation |
| \(\mathrm{(B)}\) | Threshold wavelength | \(\mathrm{(II)}\) | Stopping potential |
| \(\mathrm{(C)}\) | Maximum kinetic energy of photoelectron | \(\mathrm{(III)}\) | Maximum wavelength of an incident photon in photoelectric effect |
| \(\mathrm{(D)}\) | Quantisation of angular momentum of the electron | \(\mathrm{(IV)}\) | De-Broglie hypothesis |
| 1. | \(\mathrm{A\text-I,B\text-III,C\text- II,D\text-IV}\) |
| 2. | \(\mathrm{A\text-III,B\text-I,C\text- II,D\text-IV}\) |
| 3. | \(\mathrm{A\text-I,B\text- III,C\text-IV,D\text- II}\) |
| 4. | \(\mathrm{A\text-IV,B\text-II,C\text-I,D\text-III}\) |
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1. \(13.6\) volts
2. \(27.2\) volts
3. \(10.2\) volts
4. \(6.8\) volts
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