An electron is moving around the nucleus of a hydrogen atom in a circular orbit of radius r. What is the coulomb force between the two? \(\left ( \text{where},K=\frac{1}{4\pi \epsilon _{0}} \right )\)
1.
2.
3.
4.
When an electron transitions from n = 4 to n = 2, then the emitted line in the spectrum will be:
1. | the first line of the Lyman series. |
2. | the second line of the Balmer series. |
3. | the first line of the Paschen series. |
4. | the second line of the Paschen series. |
The total energy of an electron in the first excited state of a hydrogen atom is about –3.4 eV. Its kinetic energy in this state will be:
1. –6.8 eV
2. 3.4 eV
3. 6.8 eV
4. –3.4 eV
Assertion (A): | When light consisting of wavelengths corresponding to the Balmer series is incident on a gas containing \(He^{+}\) ions in the first three excited states - it can be absorbed by the \(He^{+}\) ions. |
Reason (R): | All the energy levels of the He+ ions are the same as those of the \(H\) atoms. |
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). |
What was Rutherford's atom according to classical theory?
1. | electrostatically stable. |
2. | electrodynamically unstable. |
3. | semi-stable. |
4. | stable. |
Assertion (A): | The hydrogen atom consists of only one electron but its emission spectrum has many lines. |
Reason (R): | Only Lyman series is found in the absorption spectrum of hydrogen atoms whereas in the emission spectrum, all the series are found. |
1. | Both (A) and (R) are true and (R) is the correct explanation of (A). |
2. | Both (A) and (R) are true but (R) is not the correct explanation of (A). |
3. | (A) is true but (R) is false. |
4. | Both (A) and (R) are false. |
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. |
The radius of the first permitted Bohr orbit for the electron in a hydrogen atom equals and its ground state energy equals -13.6 eV.
If the electron in the hydrogen atom is replaced by a muon (μ-) [ charged the same as the electron and mass 207 me], the first Bohr radius and ground state energy will be:
(\(m_e\) represents mass of electron)
1. | \(0.53 \times 10^{-13} \mathrm{~m},-3.6 \mathrm{eV}\) |
2. | \(25.6 \times 10^{-13} \mathrm{~m},-2.8 \mathrm{eV}\) |
3. | \(2.56 \times 10^{-13} \mathrm{~m},-2.8 \mathrm{keV}\) |
4. | \(2.56 \times 10^{-13} \mathrm{~m},-13.6 \mathrm{eV}\) |
Statement I: | The stationary orbits in Bohr's theory correspond to those orbits in which an integer number of de-Broglie wavelengths of the orbiting electron fit in. |
Statement II: | \(13.6\) eV cannot be absorbed by an \(H\)-atom in the ground state. | Photons having an energy greater than
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. |
When an α– particle of mass m moving with velocity v bombards a heavy nucleus of charge Ze, its distance of closest approach from the nucleus depends on m as:
1.
2.
3. m
4.