List of top Atomic and Molecular Physics Questions on Spin-orbit interaction asked in GATE PH

The spin-orbit effect splits the \( ^2p \rightarrow ^2s \) transition (wavelength, \( \lambda = 6521 \, \text{Å} \)) in Lithium into two lines with separation of \( \Delta \lambda = 0.14 \, \text{Å} \). The corresponding positive value of energy difference between the above two lines, in eV, is \( m \times 10^{-5} \). The value of \( m \) (rounded off to the nearest integer) is \(\underline{\hspace{2cm}}\). (Given: Planck's constant, \( h = 4.125 \times 10^{-15} \, \text{eV s} \), speed of light, \( c = 3 \times 10^8 \, \text{m/s} \))

The spin \( \vec{S} \) and orbital angular momentum \( \vec{L} \) of an atom precess about \( \vec{J} \), the total angular momentum. \( \vec{J} \) precesses about an axis fixed by a magnetic field \( \vec{B_1} = 2B_0 \hat{z} \), where \( B_0 \) is a constant. Now the magnetic field is changed to \( \vec{B_2} = B_0 (\hat{x} + \sqrt{2} \hat{y} + \hat{z}) \). Given the orbital angular momentum quantum number \( l = 2 \) and spin quantum number \( s = 1/2 \), \( \theta \) is the angle between \( \vec{B_1} \) and \( \vec{J} \) for the largest possible values of total angular quantum number \( j \) and its z-component \( j_z \). The value of \( \theta \) (in degree, rounded off to the nearest integer) is \(\underline{\hspace{2cm}}\).