An atom has 35 nucleons and has atomis number equal to 17 . The number of electrons with n =2 , m = 0 in it is :-

Options

A. (a)2
B. (b)4
C. (c)6
D. (d)3

Answer

To solve the question, we need to determine the number of electrons in an atom with a principal quantum number \( n = 2 \) and a magnetic quantum number \( m = 0 \). The atom has 35 nucleons and an atomic number of 17.

### Step-by-Step Solution:

1. **Identify the Atomic Number and Nucleons**:
- The atomic number (Z) is given as 17. This means the atom has 17 protons and, since it is neutral, it also has 17 electrons.
- The total number of nucleons (protons + neutrons) is given as 35.

2. **Calculate the Number of Neutrons**:
- The number of neutrons can be calculated using the formula:
\[ \text{Number of Neutrons} = \text{Nucleons} - \text{Protons} = 35 - 17 = 18 \]

3. **Determine the Element**:
- The atomic number of 17 corresponds to the element chlorine (Cl).

4. **Write the Electronic Configuration**:
- The electronic configuration of chlorine (Cl) is:
\[ 1s^2 \, 2s^2 \, 2p^6 \, 3s^2 \, 3p^5 \]
- This configuration shows how the electrons are distributed among the various orbitals.

5. **Identify Electrons with \( n = 2 \) and \( m = 0 \)**:
- The principal quantum number \( n = 2 \) corresponds to the second energy level, which includes the 2s and 2p orbitals.
- The 2s orbital can hold 2 electrons, and since it has \( l = 0 \), the only possible value for the magnetic quantum number \( m \) is 0.
- The 2p orbital can hold 6 electrons (3 sub-orbitals), with \( l = 1 \), allowing \( m \) values of -1, 0, and +1. Thus, one of the 2p sub-orbitals can also have \( m = 0 \).

6. **Count the Electrons**:
- In the 2s orbital, there are 2 electrons with \( m = 0 \).
- In the 2p orbital, there is 1 electron with \( m = 0 \) (from one of the three 2p sub-orbitals).
- Therefore, the total number of electrons with \( n = 2 \) and \( m = 0 \) is:
\[ 2 \, (\text{from } 2s) + 1 \, (\text{from } 2p) = 3 \]

### Final Answer:
The number of electrons with \( n = 2 \) and \( m = 0 \) in the atom is **3**.

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