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

Hint: 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.