Which is the correct order of increasing energy of the listed orbitals in the atom of titanium ?

Options

A. 3s< 4s< 3p <3d
B. 4s< 3s< 3p< 3d
C. 3s <3p <3d< 4s
D. 3s< 3p <4s< 3d

Explanation

To determine the correct order of increasing energy of the listed orbitals in the atom of titanium, we will use the n + l rule. This rule states that the energy of an orbital is determined by the sum of the principal quantum number (n) and the azimuthal quantum number (l). The orbital with the lower n + l value has lower energy.

### Step-by-Step Solution:

1. **Identify the orbitals**: The orbitals given are 3s, 4s, 3p, and 3d.

2. **Determine the values of n and l for each orbital**:
- For **3s**:
- n = 3, l = 0 (s orbitals have l = 0)
- n + l = 3 + 0 = **3**
- For **4s**:
- n = 4, l = 0 (s orbitals have l = 0)
- n + l = 4 + 0 = **4**
- For **3p**:
- n = 3, l = 1 (p orbitals have l = 1)
- n + l = 3 + 1 = **4**
- For **3d**:
- n = 3, l = 2 (d orbitals have l = 2)
- n + l = 3 + 2 = **5**

3. **List the orbitals with their n + l values**:
- 3s: n + l = 3
- 4s: n + l = 4
- 3p: n + l = 4
- 3d: n + l = 5

4. **Compare the n + l values**:
- The lowest value is for 3s (3), followed by 4s (4) and 3p (4), and finally 3d (5).
- Since 4s and 3p both have the same n + l value (4), we need to compare their n values:
- For 4s, n = 4
- For 3p, n = 3
- Since 4 > 3, 4s has higher energy than 3p.

5. **Establish the order of increasing energy**:
- The correct order of increasing energy is: **3s < 3p < 4s < 3d**.

### Final Answer:
The correct order of increasing energy of the listed orbitals in the atom of titanium is:
**3s < 3p < 4s < 3d**.