The maximum number of electrons that can be accommodated in an orbit is equal to __________ where n is the number of orbits.

Options

A. `4pi^(2)`
B. `2pi^(2)`
C. `(2n + 1)^(2)`
D. `pi^(2) + 4`

Explanation

To find the maximum number of electrons that can be accommodated in an orbit, we can use the formula:

**Step 1: Understand the formula for maximum electrons in an orbit.**
The maximum number of electrons (E) that can be accommodated in an orbit is given by the formula:
\[ E = 2n^2 \]
where \( n \) is the principal quantum number (the number of the orbit or shell).

**Step 2: Identify the value of n for different orbits.**
- For the first orbit (K shell), \( n = 1 \)
- For the second orbit (L shell), \( n = 2 \)
- For the third orbit (M shell), \( n = 3 \)
- For the fourth orbit (N shell), \( n = 4 \)

**Step 3: Calculate the maximum number of electrons for each orbit using the formula.**
- For K shell (n=1):
\[ E = 2(1^2) = 2 \]
- For L shell (n=2):
\[ E = 2(2^2) = 2(4) = 8 \]
- For M shell (n=3):
\[ E = 2(3^2) = 2(9) = 18 \]
- For N shell (n=4):
\[ E = 2(4^2) = 2(16) = 32 \]

**Step 4: Conclusion.**
Thus, the maximum number of electrons that can be accommodated in an orbit is given by the formula \( 2n^2 \).

**Final Answer:**
The maximum number of electrons that can be accommodated in an orbit is equal to \( 2n^2 \).

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