Q.48 The number of signals in 13
C NMR for the following structure is _____ .

The correct number of signals in the 1313C NMR spectrum of the given tricyclic cyclohexane system is 8.

Introduction

Understanding how to predict the number of 1313C NMR signals is crucial for solving competitive-exam questions on complex cyclic and polycyclic systems such as bridged cyclohexanes. In this article, the number of signals in 1313C NMR for a bridged cyclohexane skeleton is determined using symmetry analysis, equivalent carbon sets and the effect of stereogenic centres on carbon environments. The same logic can be transferred to many CSIR‑NET and GATE style structural questions.

Step 1: Interpreting the given structure

The drawing represents:

• Three fused/bridged cyclohexane rings forming a rigid tricyclic framework.

• A central bridgehead carbon bearing two hydrogens shown with solid and dashed wedges, indicating one up and one down hydrogen.

• Two additional stereogenic centres marked with wedges on the adjacent rings, giving the molecule an overall rigid, chiral, but symmetrical framework.

Because the rings are all chair‑like and locked, conformational averaging does not remove or add symmetry; only true molecular symmetry operations (rotation, reflection, inversion) matter for equivalence of carbons in 1313C NMR.

Step 2: Identifying symmetry elements

Key points for symmetry in this tricyclic system:

• There is a C22 rotational axis passing through the central bridgehead carbon and bisecting the molecule vertically.

• A 180° rotation around this axis exchanges the left and right cyclohexane rings while keeping the central carbon fixed.

• Because 1313C NMR detects carbons, any carbons that are interchanged by this C22 operation are chemically equivalent and give the same signal.

Thus, pairs of carbons related by this C22 symmetry form sets of equivalent carbons.

Step 3: Counting unique carbon environments

Consider the carbon framework qualitatively (you do not need the exact numbering for the exam, only symmetry classes):

1. Central bridgehead carbon

   • Unique position connecting the three rings and bearing two hydrogens.

   • No other carbon shares an identical environment.

   • Gives 1 signal.

2. Two equivalent bridge carbons directly attached to the central carbon (one on each side)

   • These carbons are related by the C22 axis and each connects the central carbon to a peripheral ring.

   • They are chemically equivalent.

   • Give 1 signal from this pair.

3. Two equivalent distal bridgehead carbons (top of each of the upper rings)

   • Each is at the “top” of a cyclohexane ring fused to the central framework.

   • C22 symmetry exchanges them.

   • Contribute 1 signal.

4. Four pairs of equivalent ring CH22/CH carbons on the left and right rings

   • Each carbon on the left ring has a counterpart in the right ring with identical bonding (same distance from bridgehead, same substitution pattern).

   • The C22 rotation interconverts these, so each pair gives one signal.

   • Together these four pairs provide 4 signals.

Adding these distinct environments:

• Central bridgehead: 1

• Pair of adjacent bridges: 1

• Pair of distal bridgeheads: 1

• Four ring carbon pairs: 4

Total unique 1313C environments:

$$1+1+1+4=8$$

So the number of signals in 1313C NMR is 8.

Why other possible answers would be wrong

In exam options you typically see numbers like 6, 7, 8, 9 or 10. The reasoning for rejecting the others follows directly from symmetry:

• Too few signals (e.g., 6 or 7):

  • These assume additional symmetry elements (like a mirror plane or higher rotational axis) that are not present because the stereogenic centres create a chiral, unsymmetrical orientation of substituents.

  • Therefore more carbons become inequivalent than those options allow.

• Too many signals (e.g., 9 or 10):

  • These ignore the C22 symmetry that makes left‑ and right‑side carbons equivalent.

  • Treating each ring carbon separately would overcount individual positions that are in fact magnetically equivalent.

Recognising the true point group (effectively C22 here) balances these extremes and leads to the correct count of 8.

Exam tips for similar 1313C NMR questions

• First, visualise any rotation or reflection that maps one part of the molecule onto another; such parts are equivalent and share a single 1313C signal.

• In rigid polycyclic systems, conformations are locked, so apparent left–right symmetry is often real and highly useful for reducing the number of unique carbons.

• For quick checking, count the total number of carbons, then group them into symmetry‑related sets; the number of sets equals the number of 1313C NMR signals.