How many spherical nodal surface are there in
a. a `3s` orbital
b. a `3p` orbital

Answer

To solve the question regarding the number of spherical nodal surfaces in a 3s and a 3p orbital, we can follow these steps:

### Step 1: Understand the concept of nodal surfaces
Nodal surfaces are regions in an atomic orbital where the probability of finding an electron is zero. For spherical nodal surfaces, we can use the formula:
\[ \text{Number of spherical nodes} = n - l - 1 \]
where:
- \( n \) is the principal quantum number
- \( l \) is the azimuthal quantum number

### Step 2: Determine the values of \( n \) and \( l \) for the 3s orbital
For the 3s orbital:
- The principal quantum number \( n = 3 \)
- The azimuthal quantum number \( l = 0 \) (since s orbitals have \( l = 0 \))

### Step 3: Calculate the number of spherical nodal surfaces for the 3s orbital
Using the formula:
\[ \text{Number of spherical nodes} = n - l - 1 \]
Substituting the values:
\[ \text{Number of spherical nodes} = 3 - 0 - 1 = 2 \]

### Step 4: Determine the values of \( n \) and \( l \) for the 3p orbital
For the 3p orbital:
- The principal quantum number \( n = 3 \)
- The azimuthal quantum number \( l = 1 \) (since p orbitals have \( l = 1 \))

### Step 5: Calculate the number of spherical nodal surfaces for the 3p orbital
Using the formula:
\[ \text{Number of spherical nodes} = n - l - 1 \]
Substituting the values:
\[ \text{Number of spherical nodes} = 3 - 1 - 1 = 1 \]

### Final Answer
- For the 3s orbital: **2 spherical nodal surfaces**
- For the 3p orbital: **1 spherical nodal surface**