Question

An electron will have the highest energy in which set?
A. $3,2,1,\dfrac{1}{2}$
B. $4,2, - 1,\dfrac{1}{2}$
C. $4,1,0, - \dfrac{1}{2}$
D. $5,0,0,\dfrac{1}{2}$

Answer 1

In order to answer this question, we should know about the four set of the quantum numbers of the orbitals of an atom such as principal quantum number ( $n$ ), azimuthal quantum number ( $l$ ), magnetic quantum number ( ${m_l}$ ) and spin quantum number ( ${m_s}$ ) their relation with the energy of electron

Complete answer:
We know that the foundation of chemistry starts with Bohr who established electron orbitals that are named as K, L, M, and N…. or $1,2,3$ and $4$ in ascending order. These numbers are the Principal quantum number whereas azimuthal or subsidiary quantum numbers help to determine the ellipticity of the subshell. It is denoted as ‘ $l$ ’.
We know that, $(n + l) \propto Energy$
The above equations indicate that the sum of the principal quantum number ( $n$ ) and azimuthal quantum number ( $l$ ) is directly proportional to the energy of the electrons. If the value of the $(n + l)$ is greater than the energy of the electron is also greater.
If two electrons have the same $(n + l)$ value then if the value of ‘ $n$ ’ is more then, energy will be more.
Let’s see each option.
A. $(n,l,{m_l},{m_s}) = \left( {3,2,1,\dfrac{1}{2}} \right)$
This indicates $3d$ orbital with a spin-up electron.
B. $(n,l,{m_l},{m_s}) = \left( {4,2, - 1,\dfrac{1}{2}} \right)$
This indicates $4d$ orbital with a spin-up electron.
C. $(n,l,{m_l},{m_s}) = \left( {4,1,0, - \dfrac{1}{2}} \right)$
This indicates $4{p_z}$ orbital with a spin-down electron.
D. $(n,l,{m_l},{m_s}) = \left( {5,0,0,\dfrac{1}{2}} \right)$
This indicates $5s$ orbital with a spin-up electron.
Therefore, $5s$ orbitals are clearly higher in energy than the $4d$ for most transition metals that have valence electrons in those orbitals.
Hence, the correct answer is option (B).

Note:
Always remember this relation $(n + l) \propto Energy$ which indicates that the sum of the principal quantum number ( $n$ ) and azimuthal quantum number ( $l$ ) is directly proportional to the energy of the electrons. If the value of the $(n + l)$ is greater than, the energy of the electron is also greater.