Q. No.The zero of the potential energy is so chosen that the total energy of the hydrogen atom in its \(1^{st}\) excited state is zero. Then, the energy of the ground state of the hydrogen atom is:
1.
\(-3.4~\text{eV}\)
2.
\(-6.8~\text{eV}\)
3.
\(-10.2~\text{eV}\)
4.
\(-13.6~\text{eV}\)
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| 1. | \(n=2\) state of \(\mathrm{He}^{+}\) \(\left(Z=2\right)\) ion |
| 2. | \(n=4\) state of \(\mathrm{He}^{+}\) \(\left(Z=2\right)\) ion |
| 3. | \(n=2\) state of \(\mathrm{Be}^{3+}\)\(\left(Z=4\right)\) ion |
| 4. | \(n=3\) state of \(\mathrm{Li}^{2+}\) \(\left(Z=3\right)\) ion |
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| 1. | the same phase. |
| 2. | the same energy. |
| 3. | the same direction. |
| 4. | the same phase, energy, and direction. |
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These photons can have:
| 1. | 2 possible energy values. |
| 2. | 3 possible energy values. |
| 3. | 4 possible energy values. |
| 4. | 5 possible energy values. |
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| Assertion (A): | The magnetic moment of a hydrogen-like atom is higher when it is in a state of higher quantum number \(n.\) |
| Reason (R): | The magnetic moment of hydrogen-like atom, as calculated from Bohr's theory, is directly proportional to the principal quantum number \(n.\) |
| 1. | (A) is True but (R) is False. |
| 2. | (A) is False but (R) is True. |
| 3. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
| 4. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
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| 1. | \(\dfrac he\) | 2. | \(\dfrac h{2e}\) |
| 3. | \(\dfrac {2h}e\) | 4. | \(\dfrac h{2\pi e}\) |
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1. \(13.6\) V
2. \(27.2\) V
3. \(10.2\) V
4. \(6.8\) V
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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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| 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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