The maximum number of electrons in a subshell is given by the expression

CONCEPT:

Maximum Number of Electrons in a Subshell

• The maximum number of electrons that can occupy a subshell is determined by the formula 4l + 2, where l is the azimuthal quantum number (angular momentum quantum number).
• The azimuthal quantum number (l) can take integer values from 0 to n-1, where n is the principal quantum number.

EXPLANATION:

• For a given subshell with azimuthal quantum number l:
  • The possible values of the magnetic quantum number (m_l) are from -l to +l, inclusive.
  • Each value of m_l can accommodate 2 electrons (one with spin up and one with spin down).
• Thus, the number of orbitals in a subshell is given by (2l + 1).
• Since each orbital can hold 2 electrons:
  • Maximum number of electrons = 2 * (number of orbitals).
  • = 2 * (2l + 1).
  • = 4l + 2.

Therefore, the maximum number of electrons in a subshell is given by the expression 4l + 2.