Which of the following orbitals are represented by `n=4` and `l = 1`? 

Options

A. `4p_y`
B. `4’p_x`
C. `4d_(xy)`
D. `4d_(x^2 - y^2)`

Answer

To determine which orbitals are represented by the quantum numbers \( n = 4 \) and \( l = 1 \), we can follow these steps:

### Step 1: Understand the Quantum Numbers
- The principal quantum number \( n \) indicates the shell or energy level of the electron. Here, \( n = 4 \) means we are looking at the 4th shell.
- The azimuthal quantum number \( l \) indicates the subshell type. 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
- Since \( l = 1 \), we identify the subshell as p. Therefore, the subshell for our case is the p subshell.

### Step 3: Combine the Quantum Numbers
- Now, we combine the values of \( n \) and \( l \) to determine the specific orbital. For \( n = 4 \) and \( l = 1 \), the orbital is referred to as \( 4p \).

### Step 4: Identify the Possible Orbitals
- The p subshell can contain three orbitals, which are denoted as \( 4p_x \), \( 4p_y \), and \( 4p_z \). These correspond to the different orientations of the p orbitals in three-dimensional space.

### Conclusion
- The orbitals represented by \( n = 4 \) and \( l = 1 \) are \( 4p_x \), \( 4p_y \), and \( 4p_z \). Therefore, the answer is \( 4p \) orbitals.