Q. No.The de-Broglie wavelength of an electron in the ground state of the \(\mathrm{H\text-}\)atoms is \(\lambda_1,\) while that in the \(\mathrm{He}^+\) ion is \(\lambda_2.\) The ratio \(\dfrac{\lambda_1}{\lambda_2}\) is:
1.
\(4\)
2.
\(2\)
3.
\(\dfrac12\)
4.
\(\dfrac14\)
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1. \(7.6\) eV
2. \(4.2\) eV
3. \(2.1\) eV
4. \(0.8\) eV
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1. \(12.4\) kV
2. \(6.2\) kV
3. \(24.8\) kV
4. \(37.2\) kV
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| Statement I: | The time period of revolution of an electron in its \(n^\mathrm{th}\) Bohr orbit in an atom is directly proportional to \(n^3.\) |
| Statement II: | The kinetic energy of an electron in its \(n^\mathrm{th}\) Bohr orbit in an atom is directly proportional to \(n.\) |
| 1. | Statement I is incorrect and Statement II is correct. |
| 2. | Both Statement I and Statement II are correct. |
| 3. | Both Statement I and Statement II are incorrect. |
| 4. | Statement I is correct and Statement II is incorrect. |
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1. \(13.6~\text V\)
2. \(6.8~\text V\)
3. \(27.2~\text V\)
4. \(3.4~\text V\)
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| Statement I: | The stationary orbits in Bohr's theory correspond to those orbits in which an integer number of de-Broglie wavelengths of the orbiting electron fit in. |
| Statement II: | Photons having an energy greater than \(13.6~\text{eV}\) cannot be absorbed by an \(\mathrm{H}\)-atom in the ground state. |
| 1. | Statement I is incorrect and Statement II is correct. |
| 2. | Both Statement I and Statement II are correct. |
| 3. | Both Statement I and Statement II are incorrect. |
| 4. | Statement I is correct and Statement II is incorrect. |
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1. \(1.4\) eV
2. \(0.5\) eV
3. \(0.1\) eV
4. no electrons are ejected
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(take \(Z_\text{gold}=79\) )
1. \(3\times 10^{-14}~\text m\)
2. \(3\times 10^{-13}~\text m\)
3. \(3\times 10^{-12}~\text m\)
4. \(3\times 10^{-11}~\text m\)
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1. \(13.6~\text{eV}\)
2. \(10.2~\text{eV}\)
3. \(12.75~\text{eV}\)
4. \(12.1~\text{eV}\)
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