Predict which of the following statements are true or false.
3s and 4p orbitals have same number of radial nodes.

Explanation

To determine whether the statement "3s and 4p orbitals have the same number of radial nodes" is true or false, we can follow these steps:

### Step 1: Understand Radial Nodes
A radial node is a spherical surface around the nucleus where the probability of finding an electron is zero.

**Hint:** Remember that radial nodes are related to the quantum numbers of the orbitals.

### Step 2: Know the Formula for Radial Nodes
The formula to calculate the number of radial nodes is given by:
\[ \text{Number of radial nodes} = n - l - 1 \]
where:
- \( n \) is the principal quantum number
- \( l \) is the azimuthal quantum number

**Hint:** Identify the values of \( n \) and \( l \) for the orbitals you are analyzing.

### Step 3: Calculate Radial Nodes for 3s Orbital
For the 3s orbital:
- The principal quantum number \( n = 3 \)
- The azimuthal quantum number \( l = 0 \) (since s orbitals have \( l = 0 \))

Using the formula:
\[ \text{Radial nodes for 3s} = 3 - 0 - 1 = 2 \]

**Hint:** Make sure to substitute the correct values of \( n \) and \( l \) into the formula.

### Step 4: Calculate Radial Nodes for 4p Orbital
For the 4p orbital:
- The principal quantum number \( n = 4 \)
- The azimuthal quantum number \( l = 1 \) (since p orbitals have \( l = 1 \))

Using the formula:
\[ \text{Radial nodes for 4p} = 4 - 1 - 1 = 2 \]

**Hint:** Check the values of \( n \) and \( l \) for p orbitals carefully.

### Step 5: Compare the Results
From the calculations:
- Radial nodes for 3s = 2
- Radial nodes for 4p = 2

Since both orbitals have the same number of radial nodes (2), we conclude that the statement is **True**.

**Final Answer:** The statement "3s and 4p orbitals have the same number of radial nodes" is **True**.