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Q. No.The ratio of kinetic energy and potential energy in \( 5^\text{th}\) excited state of the Hydrogen atom is:
1. \(-2\)
2. \(2\)
3. \(-\frac{1}{2}\)
4. \( \frac{1}{2}\)
Subtopic: Bohr's Model of Atom |
From NCERT
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A stationary hydrogen atom de-excites from a first excited state to the ground state. Find the recoil speed of the hydrogen atom up to the nearest integral value. (mass of hydrogen atom \(=1.8\times10^{-27}\text{kg}\))
1. \(5\)
2. \(6\)
3. \(3\)
4. \(4\)
1. \(5\)
2. \(6\)
3. \(3\)
4. \(4\)
Subtopic: Spectral Series |
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The expression for the longest wavelength in the Paschen series (for \(\mathrm{H}\) atom) is \(\dfrac{144}{xR}.\) Then the value of \({x}\) is:
(\(R\) is Rydberg’s constant).
1. \(5\)
2. \(6\)
3. \(7\)
4. \(8\)
(\(R\) is Rydberg’s constant).
1. \(5\)
2. \(6\)
3. \(7\)
4. \(8\)
Subtopic: Spectral Series |
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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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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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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 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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Both the nucleus and the atom of some element are in their respective first excited states. They get deexcited by emitting photons of wavelengths \(\lambda_ N, \lambda _A\) respectively. The ratio of their wavelength \(\frac{\lambda_N}{\lambda_A}\) is closest to:
1. \(10^{-1}\)
2. \(10^{-6}\)
3. \(10 \)
4. \(10^{-10}\)
1. \(10^{-1}\)
2. \(10^{-6}\)
3. \(10 \)
4. \(10^{-10}\)
Subtopic: Spectral Series |
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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 ratio of the shortest wavelength of Balmer series to the shortest wavelength of Lyman series for hydrogen atom is :
1. \(2:1\)
2. \(1:4\)
3. \(1:2\)
4. \(4:1\)
1. \(2:1\)
2. \(1:4\)
3. \(1:2\)
4. \(4:1\)
Subtopic: Spectral Series |
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