Question

Arrange the following in increasing energy levels.

{\text{B ) 3p < 4d < 5p < 6s < 4f}} \\\ {\text{C ) 3p < 4d < 5p < 4f < 6s}} \\\ {\text{D ) 3p < 4d < 5p < 4f < 6p}} \\\\$$

Answer 1

Higher is the $\left( {{\text{n + l}}} \right)$ value of an orbital, higher is its energy. Lower is the $\left( {{\text{n + l}}} \right)$ value of an orbital, lower is its energy. When two orbitals have equal value of $\left( {{\text{n + l}}} \right)$ then the orbital having higher value of n will have higher energy.

Complete answer:
The principal quantum number, ‘n’ can have values 1,2,3,4…. The azimuthal quantum number can have values 0,1,2,3…
Calculate $\left( {{\text{n + l}}} \right)$ value for each orbitals.
For s,p,d,f subshells, the value of azimuthal quantum number is 0,1,2,3 respectively.
For 3p orbital, the principal quantum number has value of 3 and azimuthal quantum number has value of 1. The value of $\left( {{\text{n + l}}} \right)$ is ${\text{3 + 1 = 4}}$.
For 4d orbital, the principal quantum number has value of 4 and azimuthal quantum number has value of 2. The value of $\left( {{\text{n + l}}} \right)$ is ${\text{4 + 2 = 6}}$.
For a 5p orbital, the principal quantum number has value of 5 and azimuthal quantum number has value of 1. The value of $\left( {{\text{n + l}}} \right)$ is ${\text{5 + 1 = 6}}$.
For 6s orbital, the principal quantum number has value of 6 and azimuthal quantum number has value of 0. The value of $\left( {{\text{n + l}}} \right)$ is ${\text{6 + 0 = 6}}$
For a 4f orbital, the principal quantum number has value of 4 and azimuthal quantum number has value of 3. The value of $\left( {{\text{n + l}}} \right)$ is ${\text{4 + 3 = 7}}$
Arrange the orbitals in the increasing order of $\left( {{\text{n + l}}} \right)$ value
If two orbitals have equal value of $\left( {{\text{n + l}}} \right)$ then place the orbital having higher value of n after the orbital having lower value of n.

Hence, the correct option is the option ${\text{B ) 3p < 4d < 5p < 6s < 4f}}$.

Note: According to Aufbau principle, electrons first fill the lower energy levels and then they will fill higher energy levels. In German language, the word Aufbau means building up. This rule is helpful in determining the electronic configuration of atoms/ions.