n and l for some electrons are given which of the following is expected to have least energy

Options

A. n= 3, l=2
B. n=3,l=0
C. n=2,l=1
D. n=4,l=0

Answer

To determine which electron configuration has the least energy based on the given values of n and l, we can use the n + l rule. Here’s a step-by-step solution:

### Step 1: Understand the n + l Rule
The n + l rule states that the energy of an electron in an atom can be determined by the sum of the principal quantum number (n) and the azimuthal quantum number (l). The lower the value of n + l, the lower the energy of the electron.

### Step 2: Identify the Values of n and l
For each electron configuration provided in the options, identify the values of n and l:
- **n** is the principal quantum number (shell number).
- **l** is the azimuthal quantum number (subshell type):
- s = 0
- p = 1
- d = 2
- f = 3

### Step 3: Calculate n + l for Each Option
Let's assume we have the following options with their respective n and l values:

- **Option A**: n = 3, l = 2 (3d)
- **Option B**: n = 3, l = 0 (4s)
- **Option C**: n = 2, l = 1 (3p)
- **Option D**: n = 4, l = 0 (4s)

Now, calculate n + l for each option:
- **Option A**: n + l = 3 + 2 = 5
- **Option B**: n + l = 3 + 0 = 3
- **Option C**: n + l = 2 + 1 = 3
- **Option D**: n + l = 4 + 0 = 4

### Step 4: Compare n + l Values
Now, we compare the n + l values:
- Option A: 5
- Option B: 3
- Option C: 3
- Option D: 4

### Step 5: Determine the Lowest Energy Configuration
The lowest n + l value is 3, which is found in both Option B (3s) and Option C (3p). When n + l values are equal, the configuration with the lower principal quantum number (n) has lower energy.

- Option B (3s) has n = 3.
- Option C (3p) has n = 2.

Since 2 < 3, Option C (3p) will have lower energy than Option B (3s).

### Conclusion
The electron configuration with the least energy is **Option C (3p)**.

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