Taking the bohr radius as a0=53pm, the radius of Li++ ion in its ground state on the basis of bohr's model will br about

1.53pm

2.27pm

3.18pm

4.13pm

Subtopic:  Bohr's Model of Atom |
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The binding energy of a H-atom, considering an electron moving around a fixed nucleus (proton), is,

$\mathrm{B}=-\frac{{\mathrm{me}}^{4}}{8{\mathrm{n}}^{2}{\mathrm{\epsilon }}_{0}^{2}{\mathrm{h}}^{2}}$ (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,

$\mathrm{B}=-\frac{{\mathrm{Me}}^{4}}{8{\mathrm{n}}^{2}{\mathrm{\epsilon }}_{0}^{2}{\mathrm{h}}^{2}}$ (M = proton mass)
This last expression is not correct, because,

1. 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.

Subtopic:  Bohr's Model of Atom |
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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.

Subtopic:  Bohr's Model of Atom |
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For the ground state, the electron in the H-atom has an angular momentum = $\frac{\mathrm{h}}{2\mathrm{\pi }}$, 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 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 spin of the electron

4. because electrons go around only in horizontal orbits

Subtopic:  Bohr's Model of Atom |
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O2 molecule consists of two oxygen atoms. In the molecule, nuclear force between the nuclei of the two atoms:

1. is not important because nuclear forces are short-ranged

2. is as important as electrostatic force for binding the two atoms

3. cancels the repulsive electrostatic force between the nuclei

4. is not important because oxygen nucleus have equal number of neutrons and protons

Subtopic:  Various Atomic Models |
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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

Subtopic:  Spectral Series |
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An ionised 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 ${\left(2\right)}^{4}$ times that of a H-atom
(c) the electron's orbit would go around the protons
(d) the molecule will soon decay in a proton and a H-atom

1. (a, b)

2. (a, c)

3. (b, c, d)

4. (c, d)

Subtopic:  Various Atomic Models |
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The Bohr model for the spectra of a H-atom:

(a) will not be applicable 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

1. (a, b)

2. (c, d)

3. (b, c)

4. (a, d)

Subtopic:  Bohr's Model of Atom |
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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)

Subtopic:  Spectral Series |
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Let ${E}_{n}=\frac{-1}{8{\mathrm{\epsilon }}_{0}^{2}}\frac{m{e}^{4}}{{n}^{2}{h}^{2}}$ be the energy of the nth level of H-atom. If all the H-atoms are in the ground state and radiation of frequency $\frac{\left({E}_{2}-{E}_{1}\right)}{h}$ falls on it,

(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

1. (b, d)

2. (a, d)

3. (b, c, d)

4. (c, d)

Subtopic:  Bohr's Model of Atom |
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