In any subshell, the maimum number of electrons having same value of spin quantum number is :

Options

A. `sqrt(l(l+1))`
B. `l+2`
C. `2l+1`
D. `4l+2`

Answer

To solve the question regarding the maximum number of electrons having the same value of spin quantum number in any subshell, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Quantum Numbers**:
- Each electron in an atom is described by four quantum numbers: principal quantum number (n), azimuthal quantum number (l), magnetic quantum number (m_l), and spin quantum number (m_s).

2. **Determine the Number of Orbitals in a Subshell**:
- The number of orbitals in a subshell is given by the formula \(2l + 1\), where \(l\) is the azimuthal quantum number.
- For example, if \(l = 0\) (s subshell), there is 1 orbital; if \(l = 1\) (p subshell), there are 3 orbitals; if \(l = 2\) (d subshell), there are 5 orbitals; and if \(l = 3\) (f subshell), there are 7 orbitals.

3. **Electrons in Each Orbital**:
- Each orbital can hold a maximum of 2 electrons, one with spin up (\(+\frac{1}{2}\)) and one with spin down (\(-\frac{1}{2}\)).

4. **Calculate Total Electrons in a Subshell**:
- The total number of electrons that can occupy a subshell is given by \(2 \times (2l + 1)\). This accounts for the maximum number of electrons across all orbitals in that subshell.

5. **Determine Maximum Electrons with Same Spin**:
- Since half of the electrons in the subshell will have spin up and half will have spin down, the maximum number of electrons that can have the same value of spin quantum number (either all spin up or all spin down) is half of the total number of electrons.
- Therefore, the maximum number of electrons with the same spin quantum number is \(\frac{1}{2} \times 2 \times (2l + 1) = 2l + 1\).

6. **Conclusion**:
- Thus, the maximum number of electrons in any subshell that can have the same value of spin quantum number is \(2l + 1\).

### Final Answer:
The maximum number of electrons having the same value of spin quantum number in any subshell is \(2l + 1\).