The quantum number of four electrons (el to e4) are given below :-
`{:(,n,,l,,m,,s,,),(e1,3,,0,,0,,+1//2,,),(e2,4,,0,,1,,1//2,,),(e3,3,,2,,2,,-1//2,,),(e4,3,,1,,-1,,1//2,,):}`
The correct order of decreasing energy of these electrons is :

Options

A. `e4gte3gte2gte1`
B. `e2gte3gte4gte1`
C. `e3gte2gte4gte1`
D. none

Explanation

To determine the correct order of decreasing energy of the four electrons based on their quantum numbers, we will use the n + l rule. This rule states that the energy of an electron in an atom is determined by the sum of its principal quantum number (n) and its azimuthal quantum number (l). The electron with the highest value of n + l will have the highest energy.

### Step-by-Step Solution:

1. **Identify the Quantum Numbers**:
- e1: (n=3, l=0, m=0, s=+1/2)
- e2: (n=4, l=0, m=1, s=+1/2)
- e3: (n=3, l=2, m=2, s=-1/2)
- e4: (n=3, l=1, m=-1, s=+1/2)

2. **Calculate n + l for Each Electron**:
- For e1: n + l = 3 + 0 = 3
- For e2: n + l = 4 + 0 = 4
- For e3: n + l = 3 + 2 = 5
- For e4: n + l = 3 + 1 = 4

3. **List the n + l Values**:
- e1: 3
- e2: 4
- e3: 5
- e4: 4

4. **Determine the Order of Energy Based on n + l Values**:
- The highest n + l value is for e3 (5), so it has the highest energy.
- e2 and e4 both have n + l = 4, but e2 has a higher n (4) compared to e4 (3), so e2 has higher energy than e4.
- e1 has the lowest n + l value (3), so it has the lowest energy.

5. **Final Order of Decreasing Energy**:
- e3 > e2 > e4 > e1

Thus, the correct order of decreasing energy of these electrons is:
**e3 > e2 > e4 > e1**