Which of the following is associated with the orbital designated by `n = 2,l = 1 `?

Options

A. Spherical
B. Tetrahedral
C. Dumb-shell
D. Pyramidal

Explanation

To determine which orbital is associated with the quantum numbers \( n = 2 \) and \( l = 1 \), we can follow these steps:

### Step 1: Understand the Quantum Numbers
- The principal quantum number \( n \) indicates the energy level or shell of the electron. In this case, \( n = 2 \) means we are looking at the second energy level.
- The azimuthal quantum number \( l \) defines the shape of the orbital. The values of \( l \) correspond to different subshells:
- \( l = 0 \) corresponds to the s subshell
- \( l = 1 \) corresponds to the p subshell
- \( l = 2 \) corresponds to the d subshell
- \( l = 3 \) corresponds to the f subshell

### Step 2: Identify the Subshell
- Given that \( l = 1 \), we can conclude that the subshell is a p subshell.

### Step 3: Determine the Shape of the Orbital
- The p subshell has a characteristic shape known as a "dumbbell" shape. This is a defining feature of p orbitals.

### Conclusion
- Therefore, the orbital designated by \( n = 2 \) and \( l = 1 \) is associated with a p orbital, which has a dumbbell shape.

### Final Answer
- The correct option is: **Dumbbell shape**.

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