Quantum number area assigned to get complete information of electrons regarding their energy angular momentum ,spectral lines etc. Four quantum number are known i.e principal quantum numbers which tell the distinct shell and its angular momentum .Azimuthal tell about subshell and Magnetic quantum number deals with different orbitals in subshell. spin quantum number defines the spin of electrons designated as `+(1)/(2) or-(1)/(2)`
Electrons are filled in orbitals according to Hund's rule of maximum multiplicity .
Two unpaired electrons present in carbon atom are different with respect to their :

Options

A. Principle quantum number
B. Azimuthul quantum number
C. Magnetic quantum number
D. Spin quantum number

Explanation

To solve the question regarding the quantum numbers and the differences between the two unpaired electrons in a carbon atom, we can follow these steps:

### Step 1: Understand the Quantum Numbers
The four quantum numbers that describe an electron in an atom are:
1. **Principal Quantum Number (n)**: Indicates the energy level or shell.
2. **Azimuthal Quantum Number (l)**: Indicates the subshell (s, p, d, f).
3. **Magnetic Quantum Number (m_l)**: Indicates the specific orbital within the subshell.
4. **Spin Quantum Number (m_s)**: Indicates the spin of the electron, which can be +1/2 or -1/2.

### Step 2: Determine the Electron Configuration of Carbon
Carbon has an atomic number of 6, which means it has 6 electrons. The electron configuration is:
- 1s² 2s² 2p²

### Step 3: Identify the Unpaired Electrons
In the case of carbon, the two unpaired electrons are in the 2p subshell. The 2p subshell can hold a maximum of 6 electrons, but in carbon, it has only 2 unpaired electrons.

### Step 4: Analyze the Quantum Numbers of the Unpaired Electrons
For the two unpaired electrons in the 2p subshell:
- Both electrons have the same principal quantum number (n = 2) and azimuthal quantum number (l = 1).
- The magnetic quantum number (m_l) for the 2p subshell can be -1, 0, or +1. The two unpaired electrons will occupy different orbitals in this subshell.
- The spin quantum numbers will be different for the two electrons. One will have m_s = +1/2 and the other will have m_s = -1/2.

### Step 5: Conclusion
The two unpaired electrons in a carbon atom differ in their:
- **Spin Quantum Number (m_s)**: One electron has a spin of +1/2 and the other has a spin of -1/2.

### Final Answer
The two unpaired electrons present in a carbon atom are different with respect to their **spin quantum number**.

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