How many electron in an atom with atomic number `105` can have `(n + l) = 8` ?

Options

A. 30
B. 17
C. 15
D. Un - predictable

Explanation

To determine how many electrons in an atom with atomic number 105 can have \( n + l = 8 \), we will follow these steps:

### Step 1: Identify the Electronic Configuration
The electronic configuration of the element with atomic number 105 (Dubnium) is:
\[ 1s^2 \, 2s^2 \, 2p^6 \, 3s^2 \, 3p^6 \, 3d^{10} \, 4s^2 \, 4p^6 \, 4d^{10} \, 4f^{14} \, 5s^2 \, 5p^6 \, 5d^{10} \, 5f^{14} \, 6s^2 \, 6p^6 \, 6d^3 \]

### Step 2: Understand the \( n + l \) Rule
The \( n + l \) rule states that for any electron in an atom, you can calculate \( n + l \), where \( n \) is the principal quantum number and \( l \) is the azimuthal quantum number. The values of \( l \) for different subshells are:
- \( s \): \( l = 0 \)
- \( p \): \( l = 1 \)
- \( d \): \( l = 2 \)
- \( f \): \( l = 3 \)

### Step 3: Find Subshells with \( n + l = 8 \)
We need to find all the subshells where \( n + l = 8 \):

1. **5f Subshell:**
- For 5f: \( n = 5 \) and \( l = 3 \)
- \( n + l = 5 + 3 = 8 \)
- Maximum electrons in 5f = 14

2. **6d Subshell:**
- For 6d: \( n = 6 \) and \( l = 2 \)
- \( n + l = 6 + 2 = 8 \)
- Maximum electrons in 6d = 10

### Step 4: Calculate Total Electrons
Now, we sum the maximum number of electrons from both subshells:
- Electrons in 5f = 14
- Electrons in 6d = 10

Total electrons with \( n + l = 8 \):
\[ 14 + 10 = 24 \]

### Conclusion
Thus, the total number of electrons in an atom with atomic number 105 that can have \( n + l = 8 \) is **24**.

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