List of top Atomic and Molecular Physics Questions on Atoms asked in GATE PH

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

Apart from the acoustic modes, 9 optical modes are identified from the measurements of phonon dispersions of a solid with the chemical formula \( A_nB_m \), where \( A \) and \( B \) denote the atomic species, and \( n \) and \( m \) are integers. Which of the following combinations of \( n \) and \( m \) is/are possible?

The non-relativistic Hamiltonian for a single electron atom is
\[ H_0 = \frac{p^2}{2m} - V(r) \]
where \( V(r) \) is the Coulomb potential and \( m \) is the mass of the electron.Considering the spin-orbit interaction term:
\[ H' = \frac{1}{2m^2c^2} \frac{1}{r} \frac{dV}{dr} \overrightarrow{L} \cdot \overrightarrow{S} \]
added to \( H_0 \), which of the following statements is/are true?