How many elements are accommodated in the fifth period of the long form of the periodic table ?

Options

A. 8
B. 10
C. 18
D. 32

Explanation

To determine how many elements are accommodated in the fifth period of the long form of the periodic table, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Principal Quantum Number (n)**:
- The fifth period corresponds to the principal quantum number \( n = 5 \).

2. **Choose the Correct Formula**:
- There are two formulas to calculate the number of elements in a period:
- \( \frac{n + 1}{2}^2 \times 2 \) (for odd \( n \))
- \( \frac{n + 2}{2}^2 \times 2 \) (for even \( n \))
- Since \( n = 5 \) is odd, we will use the first formula:
\[ \frac{n + 1}{2}^2 \times 2 \]

3. **Substitute \( n \) into the Formula**:
- Substitute \( n = 5 \) into the formula:
\[ \frac{5 + 1}{2}^2 \times 2 \]

4. **Calculate the Expression**:
- First, calculate \( 5 + 1 = 6 \).
- Then, calculate \( \frac{6}{2} = 3 \).
- Now, square the result: \( 3^2 = 9 \).
- Finally, multiply by 2: \( 9 \times 2 = 18 \).

5. **Conclusion**:
- Therefore, the number of elements that can be accommodated in the fifth period is **18**.

### Final Answer:
The fifth period of the long form of the periodic table accommodates **18 elements**.

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