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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.
\(\dfrac14\)
Subtopic: Bohr's Model of Atom |
Level 3: 35%-60%
Hints
Light having the wavelength equal to the first line of the Lyman series is incident on a metal having a work function of \(6\) eV. The energy of the fastest photo-electron emitted is:
| 1. | \(7.6\) eV | 2. | \(4.2\) eV |
| 3. | \(2.1\) eV | 4. | \(0.8\) eV |
Subtopic: Spectral Series |
65%
Level 2: 60%+
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What is the minimum voltage required to be applied to a Coolidge tube to generate \(X\)-rays of wavelength \(0.5~\mathring{A}?\) \((h=12.4~\text{keV-}\mathring{A}/c)\)
1. \(12.4\) kV
2. \(6.2\) kV
3. \(24.8\) kV
4. \(37.2\) kV
1. \(12.4\) kV
2. \(6.2\) kV
3. \(24.8\) kV
4. \(37.2\) kV
64%
Level 2: 60%+
Hints
Given below are two statements:
| 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. |
Subtopic: Bohr's Model of Atom |
81%
Level 1: 80%+
Hints
The product of the angular momentum and the kinetic energy of an electron in the \(n^\text{th}\) Bohr orbit in a hydrogen atom is proportional to:
| 1. | \(n\) | 2. | \(n^2\) |
| 3. | \(\dfrac1n\) | 4. | \(\dfrac{1}{n^3}\) |
Subtopic: Bohr's Model of Atom |
76%
Level 2: 60%+
Hints
The electrostatic potential at the location of an electron in the ground state of the \(\mathrm{H}\)-atom is:
1. \(13.6~\text V\)
2. \(6.8~\text V\)
3. \(27.2~\text V\)
4. \(3.4~\text V\)
1. \(13.6~\text V\)
2. \(6.8~\text V\)
3. \(27.2~\text V\)
4. \(3.4~\text V\)
Subtopic: Bohr's Model of Atom |
Level 3: 35%-60%
Hints
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Given below are two statements:
| 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. |
Subtopic: Bohr's Model of Atom |
Level 3: 35%-60%
Hints
Light, having a wavelength equal to the first line of the Balmer series, is incident onto a metal of work-function \(2\) eV. The kinetic energy of the ejected electron is:
1. \(1.4\) eV
2. \(0.5\) eV
3. \(0.1\) eV
4. no electrons are ejected
1. \(1.4\) eV
2. \(0.5\) eV
3. \(0.1\) eV
4. no electrons are ejected
Subtopic: Bohr's Model of Atom |
63%
Level 2: 60%+
Hints
In an experiment of \(\alpha\)-particle scattering by a gold foil (Geiger-Marsdon experiment), the \(\alpha\)-particles have kinetic energy \((KE=1.2\times 10^{-12}~\text J).\) What is the approximate distance of the closest approach of the \(\alpha\)-particles to the gold nuclei?
(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. \(3\times 10^{-11}~\text m\)
(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. \(3\times 10^{-11}~\text m\)
Subtopic: Various Atomic Models |
68%
Level 2: 60%+
Hints
An electron in an \(\mathrm{H}\text-\)atom makes a transition from the ground state into another state where its de-Broglie wavelength is doubled. The energy required to make this transition is:
1. \(13.6~\text{eV}\)
2. \(10.2~\text{eV}\)
3. \(12.75~\text{eV}\)
4. \(12.1~\text{eV}\)
1. \(13.6~\text{eV}\)
2. \(10.2~\text{eV}\)
3. \(12.75~\text{eV}\)
4. \(12.1~\text{eV}\)
Subtopic: Bohr's Model of Atom |
71%
Level 2: 60%+
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