If n and I are respectively the principal and azimuthal quantum numbers, then the expression for calculating the total number of electrons in any orbit is

Question

If n and I are respectively the principal and azimuthal quantum numbers, then the expression for calculating the total number of electrons in any orbit is (A) ∑ limitsl=1l=n 2(2l+1) (B) ∑ limitsl=1l=n-1 2(2l+1) (C) ∑ limitsl=0l=n+1 2(2l+1) (D) ∑ limitsl=0l=n-1 2(2l+1)

Tardigrade Admin · Accepted Answer

Total number of electrons in an orbital = 2 (2l + 1). The value of l varies from 0 to n - 1. ∴ Total numbers of electrons in any orbit= ∑ limitsl=0l=n+1 2(2l+1)

Q. If $n$ and $I$ are respectively the principal and azimuthal quantum numbers, then the expression for calculating the total number of electrons in any orbit is

$l = 1 \sum l = n 2 (2 l + 1)$

$l = 1 \sum l = n - 1 2 (2 l + 1)$

$l = 0 \sum l = n + 1 2 (2 l + 1)$

$l = 0 \sum l = n - 1 2 (2 l + 1)$

Total number of electrons in an orbital $= 2 (2 l + 1) .$
The value of $l$ varies from $0$ to $n - 1.$
$∴$ Total numbers of electrons in any orbit= $l = 0 \sum l = n + 1 2 (2 l + 1)$

Q. If n and I are respectively the principal and azimuthal quantum numbers, then the expression for calculating the total number of electrons in any orbit is

l=1∑l=n​2(2l+1)

l=1∑l=n−1​2(2l+1)

l=0∑l=n+1​2(2l+1)

l=0∑l=n−1​2(2l+1)