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Q. No.What is the minimum orbital angular momentum of an electron in a hydrogen atom?
1.
\(h\)
2.
\(\dfrac{h}{2}\)
3.
\(\dfrac{h}{2 \pi}\)
4.
\(\dfrac{h}{\lambda}\)
Subtopic: Bohr's Model of Atom |
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For a hydrogen atom, the radius of the first orbit is known as the Bohr radius \(a_0.\) For a hydrogen-like ion with \(Z\) protons, what is the radius of the \(n^\mathrm{th}\) orbit?
| 1. | \(na_0\) | 2. | \(na_0/Z\) |
| 3. | \(na_0/Z^2\) | 4. | \(n^2a_0/Z \) |
Subtopic: Bohr's Model of Atom |
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In Bohr's theory of the \(\mathrm{H}\)-atom, the de-Broglie wavelength of the electron in the \(n^{\text{th}}\) orbit is \(\lambda_n,\) while the circumference of that orbit is \(C_n.\) Then:
| 1. | \(C_n=\Large\frac{\lambda_n}{n}\) | 2. | \(C_n=n\lambda_n\) |
| 3. | \(C_n= \Large\frac{\lambda_n}{n^2}\) | 4. | \(C_n=n^2\lambda_n\) |
Subtopic: Bohr's Model of Atom |
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The figure represents the transitions between the different levels of an \(\mathrm{H}\)-atom with \(n\) representing the (principal) quantum number of the electron in that energy level. The wavelengths of the emitted photons are shown, next to the transitions.
Which of the following is true?
Which of the following is true?
| 1. | \(\lambda_{31}=\lambda_{32}+\lambda_{21}\) | 2. | \(\dfrac{1}{\lambda_{31}}=\dfrac{1}{\lambda_{32}}+\dfrac{1}{\lambda_{21}}\) |
| 3. | \(2\lambda_{32}=\lambda_{31}+\lambda_{21}\) | 4. | \(\lambda_{31}=2(\lambda_{32}+\lambda_{21})\) |
Subtopic: Spectral Series |
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The time period of revolution of the electron in the \(n^{\text{th}}\) Bohr orbit is proportional to:
| 1. | \(n^{3/2}\) | 2. | \(n^{3}\) |
| 3. | \(n^{-3}\) | 4. | \(n^{-1/3}\) |
Subtopic: Bohr's Model of Atom |
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In the given transition states, A, B and C are first, second and third exited states respectively then \({{\lambda_{1}}\over{\lambda_{2}}}={{7}\over{4n}}\), find the value of n
1. 5
2. 3
3. 7
4. 2
1. 5
2. 3
3. 7
4. 2
Subtopic: Spectral Series |
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Energy of \(He^+\) in \(2^{\text{nd}}\) orbit is \(-13.6\) eV then energy of \(Be^{+++}\) in \(n = 4\) is:
1. \(-3.4\) eV
2. \(-27.2\) eV
3. \(-13.6\) eV
4. \(-54.4\) eV
1. \(-3.4\) eV
2. \(-27.2\) eV
3. \(-13.6\) eV
4. \(-54.4\) eV
Subtopic: Bohr's Model of Atom |
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In a sample of hydrogen atoms, one atom goes through a transition \(n=3\rightarrow\) ground state with emitted wavelength \(\lambda_1\). Another atom goes through a transition \(n=2\rightarrow\) ground state with emitted wavelength \(\lambda_2\). The ratio of \(\dfrac{\lambda_1}{\lambda_2}=\)
| 1. | \(\dfrac{6}{5}\) | 2. | \(\dfrac{5}{6}\) |
| 3. | \(\dfrac{27}{32}\) | 4. | \(\dfrac{32}{27}\) |
Subtopic: Spectral Series |
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The velocity of an electron in the seventh orbit of a hydrogen-like atom is \(3.6\times 10^6\) m/s. The velocity of the electron in the \(3^{\text{rd}}\) orbit is:
1. \( 4.2 \times 10^6 ~\text{m/s} \)
2. \( 8.4 \times 10^6 ~\text{m/s} \)
3. \( 2.1 \times 10^6~\text{m/s} \)
4. \( 3.6 \times 10^6 ~\text{m/s} \)
1. \( 4.2 \times 10^6 ~\text{m/s} \)
2. \( 8.4 \times 10^6 ~\text{m/s} \)
3. \( 2.1 \times 10^6~\text{m/s} \)
4. \( 3.6 \times 10^6 ~\text{m/s} \)
Subtopic: Bohr's Model of Atom |
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The diagram shown represents different transitions of electron \(({A,B,C,D})\) between the energy levels with the energies mentioned. Among the shown transitions, which transition will generate a photon of wavelength \(124.1~\text{nm}?\)
(\(hc=1241~\text{eV-nm}\)).
1. \({A}\)
2. \({B}\)
3. \({C}\)
4. \({D}\)
(\(hc=1241~\text{eV-nm}\)).
1. \({A}\)
2. \({B}\)
3. \({C}\)
4. \({D}\)
Subtopic: Spectral Series |
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