Which of the following orbitals does not have the angular node ?

Options

A. `P_(x)` orbital
B. `d_(x^(2)` orbital
C. `P_(y)` orbital
D. `1s` orbital

Explanation

To determine which of the given orbitals does not have an angular node, we need to understand the concept of nodes in atomic orbitals. Here’s a step-by-step solution:

### Step 1: Understand the Types of Nodes
- Nodes are regions in space where the probability of finding an electron is zero.
- There are two types of nodes:
1. **Angular nodes**: These are related to the shape of the orbital and are determined by the azimuthal quantum number (l).
2. **Radial nodes**: These are related to the size of the orbital and are determined by the principal quantum number (n) and the azimuthal quantum number (l).

### Step 2: Identify the Angular Nodes
- The number of angular nodes is equal to the value of l (azimuthal quantum number).
- The formula for the total number of nodes is:
\[ \text{Total Nodes} = n - 1 \]
where n is the principal quantum number.

### Step 3: Analyze Each Orbital
- **For the px orbital**:
- l = 1 (since it's a p orbital)
- Number of angular nodes = 1
- **For the dx² orbital**:
- l = 2 (since it's a d orbital)
- Number of angular nodes = 2
- **For the py orbital**:
- l = 1 (since it's a p orbital)
- Number of angular nodes = 1
- **For the 1s orbital**:
- l = 0 (since it's an s orbital)
- Number of angular nodes = 0

### Step 4: Conclusion
- The only orbital that does not have any angular nodes is the **1s orbital**.

### Final Answer
The orbital that does not have an angular node is **1s orbital**.

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