The set of quantum numbers, n = 2, l = 2, `m_(l)` = 0 :

Options

A. (a) describes an electron in a 2s orbital
B. (b) describes one of the five orbital of a similar type
C. (c) describes an electron in a 2p orbitals
D. (d) is not allowed

Answer

To solve the question regarding the set of quantum numbers \( n = 2 \), \( l = 2 \), and \( m_l = 0 \), we will analyze each quantum number step by step.

### Step 1: Identify the Principal Quantum Number (n)
The principal quantum number \( n \) indicates the energy level or shell of an electron in an atom. In this case, \( n = 2 \) means that the electron is in the second energy level.

**Hint:** The principal quantum number corresponds to the period in the periodic table.

### Step 2: Identify the Azimuthal Quantum Number (l)
The azimuthal quantum number \( l \) determines the shape of the orbital. The values of \( l \) can be:
- \( l = 0 \) for s orbitals
- \( l = 1 \) for p orbitals
- \( l = 2 \) for d orbitals
- \( l = 3 \) for f orbitals

Since \( l = 2 \), this indicates that we are dealing with a d orbital.

**Hint:** The azimuthal quantum number defines the type of subshell.

### Step 3: Identify the Magnetic Quantum Number (m_l)
The magnetic quantum number \( m_l \) specifies the orientation of the orbital in space. The possible values of \( m_l \) range from \( -l \) to \( +l \). For \( l = 2 \), the possible values of \( m_l \) are:
- \( m_l = -2 \)
- \( m_l = -1 \)
- \( m_l = 0 \)
- \( m_l = +1 \)
- \( m_l = +2 \)

Since \( m_l = 0 \), this refers to one of the five d orbitals, specifically the \( d_{z^2} \) orbital.

**Hint:** The magnetic quantum number indicates the specific orientation of the orbital.

### Step 4: Conclusion
Given the quantum numbers \( n = 2 \), \( l = 2 \), and \( m_l = 0 \), we conclude that:
- The electron is in the 2d subshell.
- The specific orbital is one of the five d orbitals, corresponding to \( m_l = 0 \).

Now, let's evaluate the options:
1. **Describes an electron in a 2s orbital:** Incorrect, as it describes a 2d orbital.
2. **Describes one of the five orbitals of similar type:** Correct, as \( m_l = 0 \) corresponds to one of the d orbitals.
3. **Describes an electron in a 2p orbital:** Incorrect, as it describes a 2d orbital.

Thus, the correct interpretation of the quantum numbers is that they describe one of the five orbitals in the 2d subshell.

**Final Answer:** The correct option is that it describes one of the five orbitals of similar type (2d).