Q. No.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. |
1. \(0\)
2. \(1\)
3. \(2\)
4. \(3\)
1. \(K . E=|P . E |\)
2. \( K . E=\dfrac{P . E }{2}\)
3. \(K . E=|T . E |\)
4. \( P . E=-\dfrac{K . E }{2}\)
1. \(4.77~ \mathring{A}\)
2. \(0.53~ \mathring{A}\)
3. \(1.06~ \mathring{A}\)
4. \(1.59~ \mathring{A}\)
The total energy of an electron in the first excited state of the hydrogen atom is about \(-3.4\) eV. What is the kinetic energy of the electron in this state?
1. \(3.4\) eV
2. \(-3.4\) eV
3. \(3.2\) eV
4. \(-3.2\) eV
1. \(0.25\)
2. \(0.5\)
3. \(2\)
4. \(4\)
| 1. | \(3.4~\text{eV},~3.4~\text{eV}\) |
| 2. | \(-3.4~\text{eV},~-3.4~\text{eV}\) |
| 3. | \(-3.4~\text{eV},~-6.8~\text{eV}\) |
| 4. | \(3.4~\text{eV},~-6.8~\text{eV}\) |
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 |
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. \(2:3\)
| Assertion (A): | The magnetic moment of a hydrogen-like atom is higher when it is in a state of higher quantum number \(n.\) |
| Reason (R): | The magnetic moment of hydrogen-like atom, as calculated from Bohr's theory, is directly proportional to the principal quantum number \(n.\) |
| 1. | (A) is True but (R) is False. |
| 2. | (A) is False but (R) is True. |
| 3. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
| 4. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
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