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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. \(-13.6~\text{eV}\)
Subtopic: Bohr's Model of Atom |
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Whenever a photon is emitted by a hydrogen atom in the Paschen series, it is followed by further emissions of photons, in the Balmer series or the Lyman series.
These photons can have:
These photons can have:
| 1. | \(2\) possible energy values. |
| 2. | \(3\) possible energy values. |
| 3. | \(4\) possible energy values. |
| 4. | \(5\) possible energy values. |
Subtopic: Spectral Series |
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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
1. \(7.6\) eV
2. \(4.2\) eV
3. \(2.1\) eV
4. \(0.8\) eV
Subtopic: Spectral Series |
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Let \(T_1\) and \(T_2\) be the energy of an electron in the first and second excited states of hydrogen atom, respectively. According to Bohr's model of an atom, the ratio \(T_1:T_2\) is:
1. \(9:4\)
2. \(1:4\)
3. \(4:1\)
4. \(4:9\)
1. \(9:4\)
2. \(1:4\)
3. \(4:1\)
4. \(4:9\)
Subtopic: Bohr's Model of Atom |
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Let \(L_1\) and \(L_2\) be the orbital angular momentum of an electron in the first and second excited states of the hydrogen atom, respectively. According to Bohr's model, the ratio \(L_1:L_2\) is:
1. \(1:2\)
2. \(2:1\)
3. \(3:2\)
4. \(2:3\)
Subtopic: Bohr's Model of Atom |
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Given below are two statements:
| Statement I: | The time period of revolution of an electron in its \(n^\text{th}\) Bohr orbit in an atom is directly proportional to \(n^3.\) |
| Statement II: | The K.E. of an electron in its \(n^\text{th}\) 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 |
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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. \(\frac1n\)
4. \(\frac{1}{n^3}\)
1. \(n\)
2. \(n^2\)
3. \(\frac1n\)
4. \(\frac{1}{n^3}\)
Subtopic: Bohr's Model of Atom |
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The electrostatic potential at the location of an electron in the ground state of the \(H\)-atom is:
1. \(13.6\) V
2. \(6.8\) V
3. \(27.2\) V
4. \(3.4\) V
1. \(13.6\) V
2. \(6.8\) V
3. \(27.2\) V
4. \(3.4\) V
Subtopic: Bohr's Model of Atom |
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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 |
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Let \(R_1\) be the radius of the second stationary orbit and \(R_2\) be the radius of the fourth stationary orbit of an electron in Bohr's model. The ratio \(\frac{R_1}{R_2}\) is:
1. \(0.25\)
2. \(0.5\)
3. \(2\)
4. \(4\)
1. \(0.25\)
2. \(0.5\)
3. \(2\)
4. \(4\)
Subtopic: Bohr's Model of Atom |
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