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Q. No.A hydrogen atom is in an excited state of principal quantum number \((n)\). It emits a photon of wavelength \((\lambda)\) when it returns to the ground state. The value of \(n\) is:
1. \(\sqrt{\frac{\lambda R}{\lambda R-1}}\)
2. \(\sqrt{\frac{(\lambda R-1)}{\lambda R}}\)
3. \(\sqrt{\lambda(R-1)}\)
4. None of these
1. \(\sqrt{\frac{\lambda R}{\lambda R-1}}\)
2. \(\sqrt{\frac{(\lambda R-1)}{\lambda R}}\)
3. \(\sqrt{\lambda(R-1)}\)
4. None of these
Subtopic: Bohr's Model of Atom |
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The given diagram indicates the energy levels of a certain atom. When the system moves from the \(2E\) level to \(E\), a photon of wavelength \(\lambda\) is emitted. What is the wavelength of the photon produced during its transition from the \(\frac{4E}{3}\) level to \(E\)?
1. \(\frac{\lambda}{3}\)
2. \(\frac{3\lambda}{4}\)
3. \(\frac{4\lambda}{3}\)
4. \(3\lambda\)
Subtopic: Spectral Series |
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The wavenumber of a photon in the Brackett series of a hydrogen atom is \(\frac{9}{400}R.\) What is the quantum number of the electron that has transited from the orbit?
1. \(5\)
2. \(6\)
3. \(4\)
4. \(7\)
1. \(5\)
2. \(6\)
3. \(4\)
4. \(7\)
Subtopic: Spectral Series |
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Hydrogen \({}_{1}\mathrm{H}^{1}\), Deuterium \({}_{1}\mathrm{H}^{2}\), singly ionised helium \(\left({}_{2}\mathrm{He}^{4}\right)^+\), and doubly ionised lithium\(\left({}_{3}\mathrm{Li}^{6}\right)^{+++}\) all have one electron around the nucleus. Consider an electron transition from \(n=2\) to \(n=1\). If the wavelengths of emitted radiations are \(\lambda_1, \lambda_2, \lambda_3~\text{and}~\lambda_4\) respectively, then approximately which one of the following is correct?
| 1. | \(4 \lambda_1=2 \lambda_2=2 \lambda_3=\lambda_4\) |
| 2. | \( \lambda_1=2 \lambda_2=2 \lambda_3=\lambda_4\) |
| 3. | \( \lambda_1=\lambda_2=4 \lambda_3=9\lambda_4\) |
| 4. | \( \lambda_1=2\lambda_2=3 \lambda_3=\lambda_4\) |
Subtopic: Bohr's Model of Atom |
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The radius of a hydrogen atom in its ground state is \(5.3\times 10^{-11}\) m. After collision with an electron, it is found to have a radius of \(21.2\times 10^{-11}\) m. What is the principal quantum number n of the final state of the atom?
1. \(n=4\)
2. \(n=2\)
3. \(n=16\)
4. \(n=3\)
1. \(n=4\)
2. \(n=2\)
3. \(n=16\)
4. \(n=3\)
Subtopic: Bohr's Model of Atom |
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The energy of \(24.6\) eV is required to remove one of the electrons from a neutral helium atom. What is the energy (in eV) required to remove both the electrons from a neutral helium atom?
1. \(38.2\)
2. \(49.2\)
3. \(51.8\)
4. \(79.0\)
1. \(38.2\)
2. \(49.2\)
3. \(51.8\)
4. \(79.0\)
Subtopic: Bohr's Model of Atom |
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The ionisation energy of a hydrogen atom is \(13.6~\text{eV}\). Following Bohr's theory, what is the energy corresponding to a transition between the \(3^{th}\) and \(4^{th}\) orbit?
1. \(3.40~\text{eV}\)
2. \(1.51~\text{eV}\)
3. \(0.85~\text{eV}\)
4. \(0.66~\text{eV}\)
1. \(3.40~\text{eV}\)
2. \(1.51~\text{eV}\)
3. \(0.85~\text{eV}\)
4. \(0.66~\text{eV}\)
Subtopic: Bohr's Model of Atom |
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As per the Bohr model, the minimum energy (in eV) required to remove the electron from the ground state of a double ionised lithium ion (\(Z=3\)) is:
1. \(1.51\)
2. \(13.6\)
3. \(40.8\)
4. \(122.4\)
Subtopic: Bohr's Model of Atom |
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The energy of an electron in an excited hydrogen atom is \(-3.4~\text{eV}\). Its angular momentum will be:
(\(h = 6.626\times 10^{-34}\) J-s)
1. \(1.11\times 10^{34}~\text{J-s}\)
2. \(1.51\times 10^{-31}~\text{J-s}\)
3. \(2.11\times 10^{-34}~\text{J-s}\)
4. \(3.72\times 10^{-34}~\text{J-s}\)
(\(h = 6.626\times 10^{-34}\) J-s)
1. \(1.11\times 10^{34}~\text{J-s}\)
2. \(1.51\times 10^{-31}~\text{J-s}\)
3. \(2.11\times 10^{-34}~\text{J-s}\)
4. \(3.72\times 10^{-34}~\text{J-s}\)
Subtopic: Bohr's Model of Atom |
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The frequency of the series limit of the Balmer series of hydrogen atoms in terms of Rydberg constant \(R\) and velocity of light \(C\) is:
1. \(\frac{RC}{4}\)
2. \(RC\)
3. \(\frac{4}{RC}\)
4. \(4RC\)
1. \(\frac{RC}{4}\)
2. \(RC\)
3. \(\frac{4}{RC}\)
4. \(4RC\)
Subtopic: Spectral Series |
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