The number of angular nodes and radical nodes in 3s orbital are

Options

A. 0 and 2, respectively
B. 1 and 0, respectively
C. 3 and 0, respectively
D. 0 and 1, respectively

Answer

To determine the number of angular nodes and radial nodes in the 3s orbital, we can follow these steps:

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

### Step 2: Identify the Quantum Numbers for the 3s Orbital
For the 3s orbital:
- The principal quantum number (n) is 3.
- The azimuthal quantum number (l) for an s orbital is 0 (since s orbitals have a spherical shape).

### Step 3: Calculate the Number of Angular Nodes
The number of angular nodes is given by the value of l.
- Since l = 0 for the s orbital, the number of angular nodes is:
\[ \text{Number of angular nodes} = l = 0 \]

### Step 4: Calculate the Number of Radial Nodes
The number of radial nodes is calculated using the formula:
\[ \text{Number of radial nodes} = n - l - 1 \]
Substituting the values:
- n = 3
- l = 0

We get:
\[ \text{Number of radial nodes} = 3 - 0 - 1 = 2 \]

### Final Answer
Thus, for the 3s orbital:
- Number of angular nodes = 0
- Number of radial nodes = 2

### Summary
- **Angular Nodes**: 0
- **Radial Nodes**: 2