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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According to the classical electromagnetic theory, the initial frequency of the light emitted by the electron revolving around a proton in the hydrogen atom is: (The velocity of the electron moving around a proton in a hydrogen atom is \(2.2\times10^{6}\) m/s)

1. \(7.6\times10^{13}\) Hz 2. \(4.7\times10^{15}\) Hz
3.  \(6.6\times10^{15}\) Hz 4. \(5.2\times10^{13}\) Hz
Subtopic:  Bohr's Model of Atom |
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An electron in hydrogen atom makes a transition \(n_1 \rightarrow n_2\) where \(n_1\) and \(n_2\) are principal quantum numbers of the two states. Assuming Bohr's model to be valid, the time period of the electron in the initial state is eight times that in the final state. The possible values of \(n_1\) and  \(n_2\) are:
1. \( n_1 = 6~\text{and}~n_2 = 2\)
2. \( n_1 = 8~\text{and}~ n_2 = 1\)
3. \( n_1 = 8~\text{and}~ n_2 = 2\)
4. \(n_1 = 4~\text{and}~n_2 = 2\)
Subtopic:  Bohr's Model of Atom |
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A \(10~\text{kg}\) satellite circles earth once every \(2~\text{h}\) in an orbit having a radius of \(8000~\text{km}\). Assuming that Bohr’s angular momentum postulate applies to satellites just as it does to an electron in the hydrogen atom. The quantum number of the orbit of the satellite is:
1. \(2.0\times10^{43}\)
2. \(4.7\times10^{45}\)
3. \(3.0\times10^{43}\)
4. \(5.3\times10^{45}\)

Subtopic:  Bohr's Model of Atom |
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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. \(4:9\) 
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The minimum orbital angular momentum of the electron in a hydrogen atom is:
1. \(h\)
2. \(h/2\)
3. \(h/2\pi\)
4. \(h/ \lambda\)

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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. \(2:3\)

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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. \(4\)
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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

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The binding energy of a H-atom, considering an electron moving around a fixed nucleus (proton), is,

B=-me48n2ε02h2 (\(\mathrm{m}=\) 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=-Me48n2ε02h2 (\(\mathrm{M}=\) 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.

Subtopic:  Bohr's Model of Atom |
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