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Q. No.Taking the bohr radius as \(a_0=53\) pm, the radius of Li++ ion in its ground state on the basis of bohr's model will be about:
1. \(153\) pm
2. \(27\) pm
3. \(18\) pm
4. \(13\) pm
The binding energy of a H-atom, considering an electron moving around a fixed nucleus (proton), is,
\(B = - \dfrac{me^{4}}{8 n^{2} \varepsilon_{0}^{2} h^{2}}\) (\(\mathrm{m}=\) electron mass)
If one decides to work in a frame of reference where the electron is at rest, the proton would be moving around it. By similar arguments, the binding energy would be,
\(B = - \dfrac{me^{4}}{8 n^{2} \varepsilon_{0}^{2} h^{2}}\) (\(\mathrm{M}=\) proton mass)
This last expression is not correct, because,
| 1. | \(\mathrm{n}\) would not be integral. |
| 2. | Bohr-quantisation applies only to electron. |
| 3. | the frame in which the electron is at rest is not inertial. |
| 4. | the motion of the proton would not be in circular orbits, even approximately. |
The simple Bohr model cannot be directly applied to calculate the energy levels of an atom with many electrons. This is because:
| 1. | of the electrons not being subjected to a central force. |
| 2. | of the electrons colliding with each other. |
| 3. | of screening effects. |
| 4. | the force between the nucleus and an electron will no longer be given by Coulomb's law. |
For the ground state, the electron in the H-atom has an angular momentum \(\dfrac h{2\pi}\), according to the simple Bohr model. Angular momentum is a vector and hence there will be infinitely many orbits with the vector pointing in all possible directions. In actuality, this is not true,
| 1. | because the Bohr model gives incorrect values of angular momentum. |
| 2. | because only one of these would have a minimum energy. |
| 3. | angular momentum must be in the direction of the spin of the electron. |
| 4. | because electrons go around only in horizontal orbits. |
A set of atoms in an excited state decays
| 1. | in general to any of the states with lower energy |
| 2. | into a lower state only when excited by an external electric field |
| 3. | all together simultaneously into a lower state |
| 4. | to emit photons only when they collide |
An ionised \(\text H\)-molecule consists of an electron and two protons. The protons are separated by a small distance of the order of angstrom. In the ground state:
| (a) | the electron would not move in circular orbits. |
| (b) | the energy would be \(2^{4}\) times that of a \(\text H\)-atom. |
| (c) | the electron's orbit would go around the protons. |
| (d) | the molecule will soon decay in a proton and a \(\text H\)-atom. |
Choose the correct option:
| 1. | (a), (b) | 2. | (a), (c) |
| 3. | (b), (c), (d) | 4. | (c), (d) |
The Bohr model for the spectra of a \(H\)-atom:
| (a) | will not apply to hydrogen in the molecular form. |
| (b) | will not be applicable as it is for a \(He\)-atom. |
| (c) | is valid only at room temperature. |
| (d) | predicts continuous as well as discrete spectral lines. |
Choose the correct option:
| 1. | (a), (b) | 2. | (c), (d) |
| 3. | (b), (c) | 4. | (a), (d) |
The Balmer series for the H-atom can be observed:
| a. | if we measure the frequencies of light emitted when an excited atom falls to the ground state |
| b. | if we measure the frequencies of light emitted due to transitions between excited states and the first excited state |
| c. | in any transition in a H-atom |
| d. | as a sequence of frequencies with the higher frequencies getting closely packed |
1. (b, c)
2. (a, c)
3. (b, d)
4. (c, d)
Let \(E_{n} = \frac{- 1m e^{4}}{8 \varepsilon_{0}^{2}n^{2} h^{2}} \) be the energy of the \(n^\text{th}\) level of H-atom. If all the H-atoms are in the ground state and radiation of frequency \(\frac{\left(\right. E_{2} - E_{1} \left.\right)}{h}\) falls on it, then:
| (a) | it will not be absorbed at all. |
| (b) | some of the atoms will move to the first excited state. |
| (c) | all atoms will be excited to the \(n = 2\) state. |
| (d) | no atoms will make a transition to the \(n = 3\) state. |
Choose the correct option:
| 1. | (b, d) | 2. | (a, d) |
| 3. | (b, c, d) | 4. | (c, d) |
The simple Bohr model is not applicable to \(\text{He}^4\) atom because:
| (a) | \(\text{He}^4\) is an inert gas. |
| (b) | \(\text{He}^4\) has neutrons in the nucleus. |
| (c) | \(\text{He}^4\) has one more electron. |
| (d) | electrons are not subject to central forces. |
Choose the correct option:
| 1. | (a), (c) | 2. | (a), (c), (d) |
| 3. | (b), (d) | 4. | (c), (d) |
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