Question

According to the Aufbau principle, the correct order of energy of $3d$, $4s$, and $4p$ orbitals is:
(a)- $4p$ <$3d$ <$4s$
(b)- $4s$ <$4p$ <$3d$
(c)- $4s$ <$3d$ <$4p$
(d)- $3d$ <$4s$ <$4p$

Answer 1

Hint: The increasing order of energies of the various orbitals can be calculated based on \[\left( n+l \right)\] rule. n is the principal quantum number and l is the azimuthal quantum number.

Complete step by step answer:
Aufbau principle: The ‘Aufbau’ is a German word which means ‘building up’. It means the filling up of orbitals with electrons. The principle states as follows:
When the atom is in ground state, the orbitals are filled in the increasing order of their energies. In other words, electrons will first occupy the lowest-energy orbital available and enter into the higher energy orbitals only when the lower energy orbitals are filled.
The order in which the energies of the orbitals increase is:
\[\text{1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p 6s 4f 5d 6p 7s 5f 6d 7p}\]

Alternatively, the order of increasing energies of the various orbitals can be calculated based on \[\left( n+l \right)\]rule.
The energy of an orbital depends upon the sum of values, the principle quantum number (n) and the azimuthal quantum number (l). This is called the \[\left( n+l \right)\]rule.
In a neutral isolated atom, the lower the value of \[\left( n+l \right)\]for an orbital, the lower its energy. However, if the two different types of orbitals have the same value of \[\left( n+l \right)\], the orbital with a lower value of n has lower energy.
So, the correct answer is “Option C”.

Note: The azimuthal quantum number (l) for s is 0, p is 1, d is 2, and f is 3. Among $3p$ and $4s$,$3d$ has lower energy because the \[\left( n+l \right)\] value for both is 5, but $3d$ has a lower value of n.