Quantum number area assigned to get complete inforamtion of electrons regarding their energy engular momentum ,spectral lines etc. Four quantum number are known i.e pricipal quantum numbers which tell the diatence shell and its angular momentum .Azimuthal and of courase shape of orbital , Magnetic qunatum number deals with syudy of orientations or deganeracy of a subshell . spin quantum number defines te spin of electrons designaated as `+(1)/(2) or-(1)/(2)` respresented by 123 and 123 respectively .
Electrons are filled in oritals and Hun's rule of maximum multicity .
Number of electrons having the quantum numbers n=4, l=0, `s=-(1)/(2) in Zn^(+2)` ion is /are :

Options

A. `1`
B. `0`
C. `2`
D. `5`

Explanation

To solve the question regarding the number of electrons in the Zn^(+2) ion that have the quantum numbers n=4, l=0, and s=-(1/2), we can follow these steps:

### Step 1: Understand the Quantum Numbers
- The principal quantum number (n) indicates the energy level of the electron. Here, n=4 means we are looking at the 4th energy level.
- The azimuthal quantum number (l) indicates the shape of the orbital. For l=0, this corresponds to an s orbital.
- The spin quantum number (s) indicates the spin of the electron. The value s=-(1/2) indicates that we are looking for electrons with a spin down.

### Step 2: Determine the Electronic Configuration of Zn^(+2)
- The atomic number of Zinc (Zn) is 30. Therefore, the electronic configuration of neutral Zn is:
\[ \text{Zn: } [\text{Ar}] 4s^2 3d^{10} \]
- When Zinc loses 2 electrons to form Zn^(+2), the electrons are removed from the outermost shell first, which is the 4s orbital. Thus, the electronic configuration of Zn^(+2) becomes:
\[ \text{Zn}^{2+}: [\text{Ar}] 3d^{10} \]

### Step 3: Identify the Electrons in the Specified Quantum State
- We are specifically looking for electrons with the quantum numbers n=4, l=0 (which corresponds to the 4s orbital), and s=-(1/2).
- In the Zn^(+2) ion, the 4s orbital has 0 electrons because both electrons from the 4s orbital were removed when forming the Zn^(+2) ion.

### Step 4: Conclusion
- Since there are no electrons in the 4s orbital of Zn^(+2), the number of electrons with the specified quantum numbers (n=4, l=0, s=-(1/2)) is:
\[ \text{Number of electrons} = 0 \]

### Final Answer
The number of electrons having the quantum numbers n=4, l=0, and s=-(1/2) in Zn^(+2) is **0**.

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