Question

An electron can enter into the orbital when?
(A) Value of n is minimum
(B) Value of l is minimum
(C) Value of $\left( {n + l} \right)$ is minimum
(D) Value of $\left( {n + m} \right)$ is minimum

Answer 1

Hint: The filling of electrons in orbitals depends upon Aufbau’s principle. An electron always occupies the lowest energy orbital first and then enters higher energy orbitals.

Complete step by step answer:
The ‘n’ is the Principal Quantum number. It describes the average size and energy of the orbital to a greater extent.
The ‘l’ is the Azimuthal Quantum number. It describes the shape of the orbital and energy of the orbital to a greater extent.
The ‘m’ is the Magnetic Quantum number. It describes the orientation of the orbital in 3D space.
So, the energy of the orbital depends majorly on the value of ‘n’ and ‘l’. This was given by Aufbau.
Aufbau’s principle decides the filling up of electrons in orbitals. According to Aufbau’s principle, the electrons in an atom would fill principal energy levels in order of increasing energy given by (n+1) rule. The rule says that the subshell with a lower value of has lower energy and it should be filled first.
Example:- 3d- $\left( {n + l} \right)$=3+2=5
4s- $\left( {n + l} \right)$=4+0=4
Now, if we consider all options available to us then we see that in option a) only value of ‘n’ is taken minimum but we have to see the value of $(n + l)$. If the value of l is high with n minimum then the total $(n + l)$will be more. As a result, the energy will be high and the electron enters the low energy orbital. So, this can not be our answer.
In option b) we have the value of ‘l’ minimum. In this case also, if the value of ‘n’ is large then the sum is large and the energy will be again high. So, even this can not be the correct answer.
Now, the option c) has a sum $(n + l)$ value minimum. This is the correct option because when the value of the sum is less then the energy of that orbital will be lower and hence electrons will enter such an orbital first.
The given option d) is also incorrect because it considers the value of m which has no effect on the energy of the orbital.

Note: If two subshell has the same value of $\left( {n + l} \right)$ then the subshell with the lower value of ‘n’ has lower energy and it should be filled first.
Example:- 3d- $\left( {n + l} \right)$=3+2=5
4p- $\left( {n + l} \right)$=4+1=5
In this case, 3d will be filled first.