Four electrons in an atom have the set of quantum numbers as given below. Which electron is at the highest energy level ?

Options

A. (a) n = 4, l = 0, `m_(l) = 0, m_(s) = +1/2`
B. (b) n = 3, l = 0, `m_(l) = 0, m_(s) = -1/2`
C. (c) n = 3, l = 2, `m_(l) = 0, m_(s) = +1/2`
D. (d) n =4, l = 1, `m_(l) = -1, m_(s) = -1/2`

Answer

To determine which electron is at the highest energy level based on the given quantum numbers, we will follow these steps:

### Step 1: Identify the Quantum Numbers
We have four sets of quantum numbers for the electrons. Let's denote them as follows:
1. Electron 1: n = 4, l = 0
2. Electron 2: n = 3, l = 0
3. Electron 3: n = 3, l = 2
4. Electron 4: n = 4, l = 1

### Step 2: Calculate n + l for Each Electron
According to the Aufbau principle, the energy level of an electron can be determined by calculating the sum of the principal quantum number (n) and the azimuthal quantum number (l). We will calculate n + l for each electron:

1. Electron 1: n + l = 4 + 0 = 4
2. Electron 2: n + l = 3 + 0 = 3
3. Electron 3: n + l = 3 + 2 = 5
4. Electron 4: n + l = 4 + 1 = 5

### Step 3: Compare n + l Values
Now we will compare the n + l values calculated:
- Electron 1: 4
- Electron 2: 3
- Electron 3: 5
- Electron 4: 5

### Step 4: Determine Highest Energy Level
The higher the n + l value, the higher the energy level. In this case, both Electron 3 and Electron 4 have the highest n + l value of 5. However, since they have the same n + l value, we need to look at the principal quantum number (n) to determine which has the higher energy level.

- Electron 3 has n = 3 (3d subshell)
- Electron 4 has n = 4 (4p subshell)

Since n = 4 is greater than n = 3, Electron 4 is at the highest energy level.

### Conclusion
The electron at the highest energy level is **Electron 4 (n = 4, l = 1)**.

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