GATE BT 2021 • Q48
MSQ • 2 Marks
Section 2: General Biotechnology
Biomolecules, enzyme kinetics
Subtopic: Fundamentals of Biomolecules, enzyme kinetics
Question Statement:
Which of the following nucleus/nuclei is/are NMR active?
Options:
-
(A) 'H
-
(B) 13C
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(C) 160
-
(D) 325
Step-by-Step Solution & Explanation
### **Official Solution & Concept Analysis (GATE BT 2021 Q.48)**
**1. Governing Concept**:
- **Topic**: Biophysical Techniques & NMR-Active Nuclei Selection Rules
- An atomic nucleus is **NMR-active** (possesses a non-zero nuclear spin quantum number $I \neq 0$) if and only if it has an odd number of protons, an odd number of neutrons, or both:
- If **both atomic number $Z$ and mass number $A$ are even**, the nuclear spin $I = 0$ (NMR-inactive).
- Evaluating isotopes:
1. **$^1\text{H}$**: $Z=1, A=1$ (odd $A$) $\implies I = 1/2$ (**NMR-active**).
2. **$^{13}\text{C}$**: $Z=6, A=13$ (odd $A$) $\implies I = 1/2$ (**NMR-active**).
3. **$^{15}\text{N}$**: $Z=7, A=15$ (odd $A$) $\implies I = 1/2$ (**NMR-active**).
4. **$^{31}\text{P}$**: $Z=15, A=31$ (odd $A$) $\implies I = 1/2$ (**NMR-active**).
5. **$^{12}\text{C}$**: $Z=6, A=12$ (even $Z$, even $A$) $\implies I = 0$ (**NMR-inactive**).
6. **$^{16}\text{O}$**: $Z=8, A=16$ (even $Z$, even $A$) $\implies I = 0$ (**NMR-inactive**).
**2. Option Analysis**:
- **Option (A) [1H] is CORRECT**: Spin $I = 1/2$, the most common nucleus used in biological NMR.
- **Option (B) [13C] is CORRECT**: Spin $I = 1/2$, widely used in carbon heteronuclear NMR.
- **Option (C) [12C] is INCORRECT**: Spin $I = 0$ (even-even nucleus), completely NMR-silent.
- **Option (D) [16O] is INCORRECT**: Spin $I = 0$ (even-even nucleus), completely NMR-silent.
**3. Final Answer**:
- **Correct Options**: **A, B**
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