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 provided principal quantum number (n) and azimuthal quantum number (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 compared using 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: List the Given Options
We need to evaluate the following options based on their n and l values:
1. Option 1: n = 3, l = 2
2. Option 2: n = 3, l = 0
3. Option 3: n = 2, l = 1
4. Option 4: n = 4, l = 0

### Step 3: Calculate n + l for Each Option
Now, we will calculate n + l for each option:
- **Option 1**: n + l = 3 + 2 = 5
- **Option 2**: n + l = 3 + 0 = 3
- **Option 3**: n + l = 2 + 1 = 3
- **Option 4**: n + l = 4 + 0 = 4

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

### Step 5: Identify the Lowest n + l Value
The lowest n + l value is 3, which appears in both Option 2 and Option 3.

### Step 6: Determine Which Has the Least Energy
Since both Option 2 and Option 3 have the same n + l value, we need to compare their n values:
- Option 2 has n = 3
- Option 3 has n = 2

According to the n + l rule, when n + l values are the same, the option with the lower n value has lower energy. Therefore, Option 3 (n = 2, l = 1) has the least energy.

### Conclusion
The electron configuration with the least energy is given by **Option 3** (n = 2, l = 1).

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