An atom is subjected to a weak uniform magnetic field \( B \). The number of lines in its Zeeman spectrum for the transition from \( n = 2, l = 1 \) to \( n = 1, l = 0 \) is
- 8
- 10
- 12
- 5
The Correct Option is B
Solution and Explanation
Top Questions on Atoms
- Assertion (A): The potential energy of an electron revolving in any stationary orbit in a hydrogen atom is positive.
Reason (R): The total energy of a charged particle is always positive. - Prove that, in the Bohr model of the hydrogen atom, the time period of revolution of an electron in the \( n \)-th orbit is proportional to \( n^3 \).
- ........ is a potent vasodilator.
- Which one of the following corresponds to the wavelength of line spectrum of H atom in its Balmer series? (R = Rydberg constant)
- Atomicity of oxygen in ozone molecule is:
Questions Asked in GATE PH exam
“Why do they pull down and do away with crooked streets, I wonder, which are my delight, and hurt no man living? Every day the wealthier nations are pulling down one or another in their capitals and their great towns: they do not know why they do it; neither do I. It ought to be enough, surely, to drive the great broad ways which commerce needs and which are the life-channels of a modern city, without destroying all history and all the humanity in between: the islands of the past.”
(From Hilaire Belloc’s “The Crooked Streets”)
Based only on the information provided in the above passage, which one of the following statements is true?- GATE PH - 2025
- Reading Comprehension
As the police officer was found guilty of embezzlement, he was _________ dismissed from the service in accordance with the Service Rules. Select the most appropriate option to complete the above sentence.
- GATE PH - 2025
- Vocabulary
A wheel of mass \( 4M \) and radius \( R \) is made of a thin uniform distribution of mass \( 3M \) at the rim and a point mass \( M \) at the center. The spokes of the wheel are massless. The center of mass of the wheel is connected to a horizontal massless rod of length \( 2R \), with one end fixed at \( O \), as shown in the figure. The wheel rolls without slipping on horizontal ground with angular speed \( \Omega \). If \( \vec{L} \) is the total angular momentum of the wheel about \( O \), then the magnitude \( \left| \frac{d\vec{L}}{dt} \right| = N(MR^2 \Omega^2) \). The value of \( N \) (in integer) is:
- GATE PH - 2025
- Rotational Motion
- An electron with mass \( m \) and charge \( q \) is in the spin up state \[ \begin{pmatrix} 1 \\ 0 \end{pmatrix} \] at time \( t = 0 \). A constant magnetic field is applied along the \( y \)-axis, \( \mathbf{B} = B_0 \hat{j} \), where \( B_0 \) is a constant. The Hamiltonian of the system is \[ H = -\hbar \omega \sigma_y, \quad \text{where} \quad \omega = \frac{q B_0}{2m} < 0 \quad \text{and} \quad \sigma_y = \begin{pmatrix} 0 & -i \\ i & 0 \end{pmatrix}. \]
The minimum time after which the electron will be in the spin down state along the \( x \)-axis, i.e., \[ \frac{1}{\sqrt{2}} \begin{pmatrix} 1 \\ -1 \end{pmatrix}, \] is:- GATE PH - 2025
- Quantum Mechanics
The figure shows an opamp circuit with a 5.1 V Zener diode in the feedback loop. The opamp runs from \( \pm 15 \, {V} \) supplies. If a \( +1 \, {V} \) signal is applied at the input, the output voltage (rounded off to one decimal place) is:
- GATE PH - 2025
- Electrical Circuits