GATE 2024 CY – Question 27

Physical Chemistry · Spectroscopy: Atomic spectroscopy; Russell-Saunders coupling; Term symbols and spectral details; origin of selection rules. Rotational, Vibrational, Electronic and Raman spectroscopy of diatomic and simple polyatomic molecules. Line broadening and line widths; simple properties of Gaussian and Lorentzian line shapes. Molecular spectroscopy: Absorbance, Beer- Lambert’s law, Einstein’s coefficient, Jablonski diagram. Relationship of transition moment integral with molar extinction coefficient and oscillator strength. Basic principles of Nuclear Magnetic Resonance: Gyromagnetic ratio; Chemical shift, nuclear coupling. · 1 mark · Multiple select

The correct statement(s) about $^4D_{5/2}$ state of an atom is (are):

it corresponds to $L=2,S=1/2$, and $J=5/2$.
it can originate from $s^1p^2$ electronic configuration.
it splits into five levels in the presence of magnetic field.
it can show spectral transition to $^4P_{3/2}$ state.

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (D) it can show spectral transition to $^4P_{3/2}$ state.

Explanation

**Decode the term symbol $^4D_{5/2}$:** $^{2S+1}L_J$ gives
- $2S+1=4\Rightarrow S=3/2$,
- $D\Rightarrow L=2$,
- $J=5/2$.

Check each statement:
- **A. $L=2$, $S=1/2$, $J=5/2$.** False; $S=3/2$.
- **B. It can arise from $s^1p^2$.** False. With three electrons in $s^1p^2$, the quartet requires all spins parallel, which needs the two $p$ electrons to be in a triplet state ($^3P$), giving $^4P$ only, not $^4D$.
- **C. It splits into five levels in a magnetic field.** False. The number of $M_J$ levels is $2J+1=6$.
- **D. It can show a spectral transition to $^4P_{3/2}$.** True. $\Delta S=0$, $\Delta L=-1$ and $\Delta J=-1$ all satisfy the selection rules (and parity changes if the configurations differ appropriately). ✓

Answer **D**.