Which of the following is not permissible arrangement of electrons in an atom?

Q: Which of the following is not permissible arrangement of electrons in an atom?

Which of the following is not permissible arrangement of electrons in an atom?

Question

Accepted Answer

To determine which arrangement of electrons is not permissible, we need to understand the quantum numbers and their rules:

1. **Principal Quantum Number (n):** This number indicates the main energy level or shell of an electron and can take positive integer values (n = 1, 2, 3, ...).

2. **Azimuthal Quantum Number (l):** This number defines the subshell or orbital shape and can take integer values from 0 to (n-1). For example, if n = 3, then l can be 0, 1, or 2.

3. **Magnetic Quantum Number (m):** This number describes the orientation of the orbital and can take integer values from -l to +l, including zero. For example, if l = 2, then m can be -2, -1, 0, 1, or 2.

4. **Spin Quantum Number (s):** This number indicates the spin of the electron and can be either +1/2 or -1/2.

Now, let's analyze each option:

1. **Option 1: $n=3, l=2, m=-2, s=-\frac{1}{2}$**
   - Here, n = 3 allows l to be 0, 1, or 2. With l = 2, m can be -2, -1, 0, 1, or 2. The given m = -2 is valid. The spin s = -1/2 is also valid. Therefore, this arrangement is permissible.

2. **Option 2: $n=4, l=0, m=0, s=-\frac{1}{2}$**
   - Here, n = 4 allows l to be 0, 1, 2, or 3. With l = 0, m must be 0. The given m = 0 is valid. The spin s = -1/2 is also valid. Therefore, this arrangement is permissible.

3. **Option 3: $n=4, l=3, m=-3, s=+\frac{1}{2}$**
   - Here, n = 4 allows l to be 0, 1, 2, or 3. With l = 3, m can be -3, -2, -1, 0, 1, 2, or 3. The given m = -3 is valid. The spin s = +1/2 is also valid. Therefore, this arrangement is permissible.

4. **Option 4: $n=3, l=2, m=-3, s=-\frac{1}{2}$**
   - Here, n = 3 allows l to be 0, 1, or 2. With l = 2, m can be -2, -1, 0, 1, or 2. The given m = -3 is not valid because it falls outside the permissible range for m when l = 2. Therefore, this arrangement is not permissible.

In conclusion, Option 4 is the correct answer because it violates the rule for the magnetic quantum number (m) given the azimuthal quantum number (l). The value of m = -3 is not allowed when l = 2, making this arrangement of electrons not permissible.