If elements of quantum number greater than `n` were not allowed , the number of possible electrons in nature would be ?

Options

A. `(1)/(2)n(n+1)`
B. `{(n(n+1))/(2)}^2`
C. `(1)/(2)n(n+1)(2n+1)`
D. `(1)/(3)n(n+1)(2n+1)`

Answer

D

Explanation

For each principal quantum number n, number of electrons permitted equals the number of elements corresponding to the quantum number .
`({:("Total number"),("of electrons"):})= sumn=(n(n+1)(2n+1))/(3)`