Statement I: | \(n^\text{th}\) Bohr orbit in an atom is directly proportional to \(n^3.\) | The time period of revolution of an electron in its
Statement II: | \(n^\text{th}\) Bohr orbit in an atom is directly proportional to \(n.\) | The K.E of an electron in its
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. |
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 |
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. | \(n_1 = 4~\text{and}~n_2 = 2\) |
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. \(5.3\times10^{45}\)
The minimum orbital angular momentum of the electron in a hydrogen atom is:
1. \(h\)
2. \(h/2\)
3. \(h/2\pi\)
4. \(h/ \lambda\)
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. \(2:3\)
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. |