Q. No.Using Bohr's model, calculate the ratio of the magnetic field generate due to the motion of the electrons in the \(2^{nd}\) and \(4^{th}\) orbits of hydrogen atom.
1. \(1:1\)
2. \(32:2\)
3. \(16:3\)
4. \(32:1\)
1. \(1:1\)
2. \(32:2\)
3. \(16:3\)
4. \(32:1\)
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The ratio of momentum of the photons of the \(1^\text{st}\) and \(2^\text{nd}\) line of Balmer series of Hydrogen atoms is \(\alpha / \beta .\) The possible values of \(\alpha\) and \(\beta\) are:
1. \(27~\text{and}~20\)
2. \(3~\text{and}~16\)
3. \(5~\text{and}~36\)
4. \(20~\text{and}~27\)
1. \(27~\text{and}~20\)
2. \(3~\text{and}~16\)
3. \(5~\text{and}~36\)
4. \(20~\text{and}~27\)
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Angular momentum of an electron in a hydrogen atoms is \(\dfrac{3 {h}}{\pi}\), then the energy electron is: (in eV)
1. \(-1.51\)
2. \(-0.85\)
3. \(-0.38\)
4. \(-0.28\)
1. \(-1.51\)
2. \(-0.85\)
3. \(-0.38\)
4. \(-0.28\)
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The energy of an electron in an orbit of the Bohr’s atom is \(-0.04 {E}_0 ~\text{eV}\) where \(E_0\) is the ground state energy. If \(L\) is the angular momentum of the electron in this orbit and \(h\) is the Planck’s constant, then \(\dfrac{2 \pi {L}}{h}\) is:
1. \(2\)
2. \(4\)
3. \(5\)
4. \(6\)
1. \(2\)
2. \(4\)
3. \(5\)
4. \(6\)
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Two electrons are moving in orbits of two hydrogen like atoms with speeds \(3\times10^5~\text{m/s} \) and \(2.5\times10^5~\text{m/s}\) respectively. If the radii of these orbits are nearly the same, then the possible order of energy are, respectively:
1. \(6\) and \(5\)
2. \(9\) and \(8\)
3. \(8\) and \(10\)
4. \(10\) and \(12\)
1. \(6\) and \(5\)
2. \(9\) and \(8\)
3. \(8\) and \(10\)
4. \(10\) and \(12\)
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Given below are two statements:
In the light of the above statements, choose the most appropriate answer from the options given below:
| Statement (I): | The dimensions of Planck's constant and angular momentum are same. |
| Statement (II): | In Bohr's model electron revolve around the nucleus only in those orbits for which angular momentum is integral multiple of Planck's constant. |
| 1. | Both Statement I and Statement II are incorrect |
| 2. | Statement I is incorrect but Statement II is correct |
| 3. | Statement I is correct but Statement II is incorrect |
| 4. | Both Statement I and Statement II are correct |
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Considering the Bohr model of hydrogen like atoms, the ratio of the radius of \(5 ^{th}\) orbit of the electron in \(\mathrm{Li}^{2+}\) and \(\mathrm{He}^+ \) is:
1. \(\dfrac{3}{2} \)
2. \(\dfrac{4}{9} \)
3. \(\dfrac{9}{4} \)
4. \(\dfrac{2}{3 }\)
1. \(\dfrac{3}{2} \)
2. \(\dfrac{4}{9} \)
3. \(\dfrac{9}{4} \)
4. \(\dfrac{2}{3 }\)
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An electron in the hydrogen atom initially in the fourth excited state makes a transition to \( n^\text{th}\) energy state by emitting a photon of energy \(2.86 ~\text{eV}.\) The integer value of \(n\) will be:
1. \(2\)
2. \(10\)
3. \(6\)
4. \(15\)
1. \(2\)
2. \(10\)
3. \(6\)
4. \(15\)
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Given below are two statements:
Choose the correct answer from the options given below:
| Assertion (A): | The Bohr model is applicable to hydrogen and hydrogen-like atoms only. |
| Reason (R): | The formulation of Bohr model does not include repulsive force between electrons. |
| 1. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
| 2. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
| 3. | (A) is True but (R) is False. |
| 4. | (A) is False but (R) is True. |
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In hydrogen like ion, the energy difference between the \(2^\text{nd}\) excitation energy state and ground is \(108.8~\text{eV}.\) The atomic number of the ion is:
1. \(1\)
2. \(2\)
3. \(3\)
4. \(4\)
1. \(1\)
2. \(2\)
3. \(3\)
4. \(4\)
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