Question

The maximum number of electrons theoretically possible for a seventh principal quantum number is:
(A) $ 49 $
(B) $ 196 $
(C) $ 86 $
(D) $ 98 $

Answer 1

Hint: The principal quantum number basically has positive values like $ 1,2,3.... $ It concludes the size and energy of every orbitals. Orbitals having the same values as that of principal quantum numbers form a shell.

Complete step by step solution:
Basically, we can determine the number of electrons present by using principal quantum number
For $ {n^{th}} $ shell we have $ 2{n^2} $ electrons in it
Where $ n $ denotes principal quantum number
So, to find out maximum number of electrons seventh principal quantum number can have is:
For $ n = 7 $
 $ 2{n^2} = 2{(7)^2} $ $ 2(49) = 98 $
Hence, the maximum number of electrons in seventh principal quantum number is $ 98 $ electrons.
The correct option is D.

Note:
Principal quantum number cannot describe the exact location of the electron but it basically gives us the highest probability to find the electron. It is basically defined as the distance between the nucleus and the electron.