Q. No.As an electron makes a transition from an excited state to the ground state of a hydrogen-like atom/ion:
| 1. | its kinetic energy increases but potential energy and total energy decrease |
| 2. | kinetic energy, potential energy and total energy decrease |
| 3. | kinetic energy decreases, potential energy increases but total energy remains same |
| 4. | kinetic energy and total energy decrease but potential energy increases |
Subtopic: Bohr's Model of Atom |
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If one were to apply the Bohr model to a particle of mass '\(m\)' and charge '\(q\)' moving in a plane under the influence of a magnetic field '\(B\)', the energy of the charged particle in the \(n^\text{th}\) level will be:
1. \({n}\left(\frac{{hqB}}{4 \pi {m}}\right) \)
2. \({n}\left(\frac{{hqB}}{\pi{m}}\right)\)
3. \({n}\left(\frac{{hqB}}{2 \pi {m}}\right)\)
4. \({n}\left(\frac{{hqB}}{8 \pi {m}}\right)\)
1. \({n}\left(\frac{{hqB}}{4 \pi {m}}\right) \)
2. \({n}\left(\frac{{hqB}}{\pi{m}}\right)\)
3. \({n}\left(\frac{{hqB}}{2 \pi {m}}\right)\)
4. \({n}\left(\frac{{hqB}}{8 \pi {m}}\right)\)
Subtopic: Bohr's Model of Atom |
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According to Bohr's theory, the time-averaged magnetic field at the centre (i.e. nucleus) of a hydrogen atom due to the motion of electrons in the \({n}^\text{th}\) orbit is proportional to:
(\(n=\) principal quantum number)
1. \({n}^{-5}\)
2. \({n}^{-4}\)
3. \({n}^{-3}\)
4. \({n}^{-2}\)
(\(n=\) principal quantum number)
1. \({n}^{-5}\)
2. \({n}^{-4}\)
3. \({n}^{-3}\)
4. \({n}^{-2}\)
Subtopic: Bohr's Model of Atom |
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The acceleration of an electron in the first orbit of the hydrogen atom \({(n = 1})\) is:
1. \(\frac{h^2}{\pi^2m^2r^3}\)
2. \(\frac{h^2}{4\pi^2m^2r^3}\)
3. \(\frac{h^2}{4\pi m^2r^3}\)
4. \(\frac{h^2}{8\pi^2m^2r^3}\)
1. \(\frac{h^2}{\pi^2m^2r^3}\)
2. \(\frac{h^2}{4\pi^2m^2r^3}\)
3. \(\frac{h^2}{4\pi m^2r^3}\)
4. \(\frac{h^2}{8\pi^2m^2r^3}\)
Subtopic: Bohr's Model of Atom |
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The energy required to remove the electron from a singly ionized helium atom is \(2.2\) times the energy required to remove an electron from a helium atom. The total energy required to ionize the helium atom completely is:
1. \(34~\text{eV}\)
2. \(20~\text{eV}\)
3. \(79~\text{eV}\)
4. \(109~\text{eV}\)
1. \(34~\text{eV}\)
2. \(20~\text{eV}\)
3. \(79~\text{eV}\)
4. \(109~\text{eV}\)
Subtopic: Bohr's Model of Atom |
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The de-Broglie wavelength \((\lambda _B)\) associated with the electron orbiting in the second excited state of a hydrogen atom is related to that in the ground state \((\lambda _G)\) by:
1. \( \lambda _B = 3\lambda _G\)
2. \( \lambda _B = 2\lambda _G\)
3. \( \lambda _B = 3\lambda _{G/3}\)
4. \( \lambda _B = 3\lambda _{G/2}\)
1. \( \lambda _B = 3\lambda _G\)
2. \( \lambda _B = 2\lambda _G\)
3. \( \lambda _B = 3\lambda _{G/3}\)
4. \( \lambda _B = 3\lambda _{G/2}\)
Subtopic: Bohr's Model of Atom |
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A \(\mathrm{He}^+\) ion is in its first excited state. Its ionization energy is:
1. \(48.36~\text{eV}\)
2. \(13.60~\text{eV}\)
3. \(54.40~\text{eV}\)
4. \(6.04~\text{eV}\)
Subtopic: Bohr's Model of Atom |
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The recoil speed of a hydrogen atom after it emits a photon in going from \(n=5\) state to \(n =1\) state will be:
1. \(4.17\) m/s
2. \(2.19\) m/s
3. \(3.25\) m/s
4. \(4.34\) m/s
Subtopic: Bohr's Model of Atom |
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In Bohr's atomic model of hydrogen, let \(K,P\) and \(E\) be the kinetic energy, potential energy and total energy of the electron respectively. Choose the correct option when the electron undergoes transitions to a higher level:
| 1. | All \(K,P\) and \(E\) increase |
| 2. | \(K\) decreases, \(P\) and \(E\) increase |
| 3. | \(P\) decreases, \(K\) and \(E\) increase |
| 4. | \(K\) increases, \(P\) and \(E\) decrease |
Subtopic: Bohr's Model of Atom |
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The ratio of the speed of the electron in the \(3^{\mathrm{rd}}\) orbit of \(\mathrm{He}^{+}\) to the speed of the electron in the \(3^{\mathrm{rd}}\) orbit of the hydrogen atom will be:
1. \(1:1\)
2. \(1:2\)
3. \(4:1\)
4. \(2:1\)
1. \(1:1\)
2. \(1:2\)
3. \(4:1\)
4. \(2:1\)
Subtopic: Bohr's Model of Atom |
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