Question

If elements of quantum number greater than ${}^{\prime }{n}^{\prime }$ were not allowed, the number of possible elements in nature would have been

• A. $\frac{1}{2}n(n+1)$
• B. ${\left\{\frac{n(n+1)}{2}\right\}}^2$
• C. $\frac{1}{6}n(n+1)(2n+1)$
• D. $\frac{1}{3}n(n+1)(2n+1)$

Answer 1

The correct option is D $\frac{1}{3}n(n+1)(2n+1)$

$n^{th}$ shell can hold upto $2n^2$ electrons
Total number of possible elements would be ${\sum }_1^{n}2n^2$$=\frac{n}{3}(n+1)(2n+1)$