Question

How many electrons can fit in the orbital for which n=3 and l = 1?
A) 10
B) 14
C) 2
D) 6

Answer 1

Hint: Using the given value of the principal quantum number and angular quantum number determine the orbital notation. Using the value of the angular quantum number determines the number of possible orbitals. Each orbital can occupy a maximum of 2 electrons.

Complete step by step answer:
Quantum numbers are used to describe completely the position, energy, space orientation and possible interaction of electrons in an atom. There are four types of quantum numbers:
- Principal quantum number (n)
- Angular quantum number (l)
- Magnetic quantum number (m)
- Spin quantum number (s)
Here, we have given n=3 and l = 1.
So, we have given values of principal quantum number and angular quantum number.
The principal quantum number (n) denotes the energy level or the principal shell to which electron belongs. It gives an idea of the size of the shell and hence the energy of the orbit.
Here, n=3 indicates electrons are present in energy level 3.
The angular quantum number (l) denotes the subshell to which the electron belongs and also its angular momentum in its motion around the nucleus. It determines the shape of the orbital.
l = 0,1,2,3 indicates s, p, d, f sub-shell respectively.
We have given l =1 that indicates electrons are present in subshell p.
So, n=3 and l = 1 indicates electrons are present in the 3p subshell.
The number of orbitals for a given value of an angular quantum number can be calculated using the formula
 (\[{\text{2l + 1)}}\].
Here the value of l is 1
So, \[{\text{(2l + 1) = 3}}\]
The p subshell has a maximum of 3 orbitals and each orbital contains a maximum of 2 electrons.
So, a maximum of 6 electrons fit in the orbital for which n=3 and l = 1

Hence, the correct option is (D) 6.

Note: The p sub-shell is a dumb-bell shape. The p subshell has 3 orbital \[{{\text{p}}_{\text{x}}}{\text{,}}{{\text{p}}_{{\text{y }}}}{\text{and }}{{\text{p}}_{\text{z}}}\]. Each orbital occupies 2 electrons with opposite spin according to the pauli exclusion principle.