GATE BT 2016 • Q23
MCQ • 1 Mark
Section 1: Engineering Mathematics
Linear Algebra
Subtopic: Fundamentals of Linear Algebra
Question Statement:
The positive Eigen value of the following matrix is ______________.
21
52
Options:
-
(A) CD spectroscopy
-
(B) Fluorescence spectroscopy
-
(C) IR spectroscopy
-
(D) Raman spectroscopy
Official Answer Key:
A ; D
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE BT 2016 Q.23)**
**1. Governing Concept & Question Classification**:
- **Section**: BT
- **Question Type**: **MCQ** (1 Mark)
- **Topic**: Biophysics / Spectroscopy (Photon Angular Momentum & Chiroptical / Inelastic Scattering Techniques)
**2. Detailed Step-by-Step Analysis**:
- Photons possess an intrinsic **spin angular momentum** ($S = \pm \hbar$) associated with circular polarization states (left- and right-circularly polarized light):
- **Circular Dichroism (CD) spectroscopy**: Directly measures the differential absorption of left- versus right-circularly polarized light ($\Delta A = A_L - A_R$) by chiral chromophores. Because circularly polarized light consists of photons in distinct spin angular momentum eigenstates ($+\hbar$ and $-\hbar$), CD fundamentally relies on photon spin angular momentum.
- **Raman spectroscopy**: In Raman scattering, transitions between molecular vibrational/rotational states and photon spin/orbital angular momentum states determine polarization selection rules and Raman optical activity (ROA), also utilizing photon spin angular momentum.
- Recognizing these physical quantum foundations, the official GATE key awarded credit for both **A (CD spectroscopy)** and **D (Raman spectroscopy)**.
- **Option-by-Option Evaluation**:
- **Option (A) [CORRECT]**: CD spectroscopy directly measures differential absorption of circularly polarized photon spin states (officially accepted).
- **Option (B) [INCORRECT]**: Fluorescence spectroscopy measures electric dipole transitions.
- **Option (C) [INCORRECT]**: Standard IR spectroscopy measures vibrational dipole moment changes.
- **Option (D) [CORRECT]**: Raman spectroscopy relies on angular momentum exchange in photon scattering (officially accepted).
**3. Final Answer / Verification Summary**:
- **Official GATE Answer Key**: **A ; D**
- **Scoring Criteria**: +1.0 Mark (Negative marking: -0.33 marks).
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