After filling of np orbital, the next orbital filled will be

Options

A. `(n+1)s`
B. (n+2)p
C. (n+1)d
D. (n+2)s

Answer

To determine which orbital is filled after the np orbital, we can use the Aufbau principle, which states that electrons fill orbitals in order of increasing energy, defined by the sum of the principal quantum number (n) and the azimuthal quantum number (l).

### Step-by-Step Solution:

1. **Identify the Quantum Numbers for np Orbital**:
- The np orbital has a principal quantum number \( n \) and an azimuthal quantum number \( l = 1 \) (since p orbitals correspond to \( l = 1 \)).
- Therefore, for the np orbital, we have:
\[ n + l = n + 1 \]

2. **Calculate n + l for Possible Next Orbitals**:
- We need to calculate \( n + l \) for the next possible orbitals:
- **n + 1 s orbital**:
- Here, \( n + 1 \) is the principal quantum number and \( l = 0 \) for s orbitals.
- Thus, \( n + l = (n + 1) + 0 = n + 1 \).
- **n + 2 p orbital**:
- Here, \( n + 2 \) is the principal quantum number and \( l = 1 \).
- Thus, \( n + l = (n + 2) + 1 = n + 3 \).
- **n + 1 d orbital**:
- Here, \( n + 1 \) is the principal quantum number and \( l = 2 \).
- Thus, \( n + l = (n + 1) + 2 = n + 3 \).
- **n + 2 f orbital**:
- Here, \( n + 2 \) is the principal quantum number and \( l = 3 \).
- Thus, \( n + l = (n + 2) + 3 = n + 5 \).

3. **Compare the n + l Values**:
- From the calculations:
- np orbital: \( n + 1 \)
- n + 1 s orbital: \( n + 1 \)
- n + 2 p orbital: \( n + 3 \)
- n + 1 d orbital: \( n + 3 \)
- n + 2 f orbital: \( n + 5 \)

4. **Determine the Next Orbital to be Filled**:
- The lowest value of \( n + l \) after filling the np orbital is for the n + 1 s orbital, which is equal to \( n + 1 \).
- Therefore, the next orbital to be filled after the np orbital is the **n + 1 s orbital**.

### Final Answer:
The next orbital filled after the np orbital will be the **n + 1 s orbital**.