What is the half of the maximum number of electrons in any shell, if n is the orbit number?

The correct answer is n².

• The maximum number of electrons that can be present in a shell is given by the formula 2n ².

\(\Rightarrow {2n^2 \over 2} = n^2\)

• Half of the maximum is n 2.
• ‘n’ is the orbit number or energy level index, i.e. 1, 2, 3,….
• According to the given formula −
• First orbit i.e. K-shell will be = 2 × 1² = 2
• Second orbit i.e. L-shell will be = 2 × 2² = 8
• Third orbit i.e. M-shell will be = 2 × 3² = 18
• Fourth orbit i.e. N-shell will be = 2 × 4² = 32

Notes:

• Electronic configuration filled according to the Aufbau principle.
• Aufbau Principle:
  • It states that electrons are filled into atomic orbitals in the increasing order of orbital energy levels.
  • The order of energy level is 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p, and so on.

Mistake Points

The question asked for half the total maximum- 

∴ instead of 2n² we go with, n²