Electronic configuration of multielectron atoms can be written by the use of four quantum numbers and also by following certain principles. Pauli's exclusion principle suggests that maximum capacity of an atomic orbital is two. Auf bau principle suggests that the lower energy orbitals are filled first and hence stability can be attained. Hunds rule of maximum multiplicity suggests that pairing occurs with one electron. The arrangement of electrons in the space around the nucleus can be understood only after writing the electronic configuration. Thus writing electronic configuration is more important in the structure of an atom. The set of quantum numbers not possible for electrons present in potassium atom in its ground state

Options

A. `n=2, l=1, m=+1, s = +(1)/(2)`
B. `n=3, l=0, m = 0, s = -(1)/(2)`
C. `n=3, l=2, m=-1, s = +(1)/(2)`
D. `n=4, l=0, m=0, s = +(1)/(2)`

Answer

To determine the set of quantum numbers that is not possible for the electrons present in a potassium atom in its ground state, we need to follow these steps:

### Step 1: Identify the Atomic Number
The atomic number of potassium (K) is 19. This means that a neutral potassium atom has 19 electrons.

### Step 2: Write the Electronic Configuration
The electronic configuration for potassium can be written as follows:
- Fill the 1s orbital: 1s²
- Fill the 2s orbital: 2s²
- Fill the 2p orbital: 2p⁶
- Fill the 3s orbital: 3s²
- Fill the 3p orbital: 3p⁶
- Finally, fill the 4s orbital: 4s¹

Thus, the complete electronic configuration for potassium is:
\[ \text{1s}^2 \, \text{2s}^2 \, \text{2p}^6 \, \text{3s}^2 \, \text{3p}^6 \, \text{4s}^1 \]

### Step 3: Determine the Quantum Numbers
Each electron in an atom can be described by a set of four quantum numbers: \( n \) (principal quantum number), \( l \) (azimuthal quantum number), \( m_l \) (magnetic quantum number), and \( s \) (spin quantum number).

- For the 1s orbital:
- \( n = 1 \), \( l = 0 \) (s orbital)
- For the 2s orbital:
- \( n = 2 \), \( l = 0 \) (s orbital)
- For the 2p orbital:
- \( n = 2 \), \( l = 1 \) (p orbital)
- For the 3s orbital:
- \( n = 3 \), \( l = 0 \) (s orbital)
- For the 3p orbital:
- \( n = 3 \), \( l = 1 \) (p orbital)
- For the 4s orbital:
- \( n = 4 \), \( l = 0 \) (s orbital)

### Step 4: Identify Possible Values of Quantum Numbers
From the electronic configuration, we can summarize the possible quantum numbers for potassium:
- \( n = 1, 2, 3, 4 \)
- \( l = 0 \) (s orbital), \( l = 1 \) (p orbital)

### Step 5: Identify the Invalid Quantum Number Set
The azimuthal quantum number \( l \) can take values of 0 (s), 1 (p), and 2 (d). However, since potassium does not have any electrons in the d orbital (as it is filled up to 4s), \( l = 2 \) is not possible.

### Conclusion
The set of quantum numbers that is not possible for the electrons present in the potassium atom in its ground state is:
- \( n = 3 \), \( l = 2 \), \( m_l = -1 \), \( s = +\frac{1}{2} \)