If n and `l` are respectively the rpincipal and azimuthal quantum numbes , then the expression for calculating the total number of electrons in any energy level is :

Options

A. `underset (l=n+1) underset(l=1) overset(l=n)(sum2(2l+1)`
B. `underset (l=n+1) underset(l=1-1) overset(l=n)(sum2(2l+1)`
C. `underset(l=0) (sum2(2l+1)`
D. ` underset(l=0) (sum2(2l+1)`

Answer

D

Explanation

Total velue of electrons in a subshell
`= 2 (2l +1)` where l vatires form O to `n- 1`
`l = n-1 l = n-1`
`:. underset(l=0)(sum2) (2l+1) =underset(l=0)( 2sum) (l +n)`

`= 2 [ 2 { (n(n-1))/2} +n]`
`= 2 n [n-1 +1 ] = 2n^2`
The total no. of electrons in a shell.
`:. l=n-1`
`:. sum 2 (2l +1) = 2n^2`
` l=0`.