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

Options

A. 30
B. 17
C. 15
D. Unpredictable

Explanation

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

### Step 1: Identify the Element
The atomic number 105 corresponds to the element Dubnium (Db).

### Step 2: Determine the Electronic Configuration
The electronic configuration of Dubnium is:
\[ \text{Rn} \, 5f^{14} \, 6d^3 \, 7s^2 \]
This means Dubnium has electrons in the following orbitals:
- 5f: 14 electrons
- 6d: 3 electrons
- 7s: 2 electrons

### Step 3: Calculate \( n + l \) for Each Orbital
We need to calculate the \( n + l \) values for the orbitals present in Dubnium:
- For the **5f** orbital:
- \( n = 5 \)
- \( l = 3 \) (since f corresponds to \( l = 3 \))
- \( n + l = 5 + 3 = 8 \)

- For the **6d** orbital:
- \( n = 6 \)
- \( l = 2 \) (since d corresponds to \( l = 2 \))
- \( n + l = 6 + 2 = 8 \)

- For the **7s** orbital:
- \( n = 7 \)
- \( l = 0 \) (since s corresponds to \( l = 0 \))
- \( n + l = 7 + 0 = 7 \) (does not satisfy \( n + l = 8 \))

### Step 4: Count the Electrons for Valid Orbitals
Now we will count the number of electrons in the orbitals that satisfy \( n + l = 8 \):
- **5f** has 14 electrons.
- **6d** has 3 electrons.

### Step 5: Total the Electrons
The total number of electrons that can have \( n + l = 8 \) is:
\[ 14 \, (\text{from } 5f) + 3 \, (\text{from } 6d) = 17 \]

### Final Answer
Thus, the total number of electrons in Dubnium (atomic number 105) that can have \( n + l = 8 \) is **17**.

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