Question

If the Aufbau principle is not followed, the atomic number of the first f-block element will be:
A. 55
B. 47
C. 31
D. 57

Answer 1

Hint: Aufbau principle follows the \[\left( {n + l} \right)\] rule to fill the subshells and we get the atomic number of first f-block element as 57 but if this rule is not followed then, we will not fill electrons by considering the increasing values of \[\left( {n + l} \right)\]

Complete step by step answer:
First of all, we need to understand a little about the Aufbau principle. The Aufbau principle states that the electrons are first filled into the lower energy orbitals and then in higher energy orbitals in the ground state of that atom. This is done to attain a stable electronic configuration of the element.
The orbitals are filled by considering the two general rules mentioned below:
Electrons are first filled in orbitals with the lowest value of \[\left( {n + l} \right)\].
If two orbitals have the same value of \[\left( {n + l} \right)\], then the electron goes to the one with lower n value.
Here, n is the principal quantum number,
l is the azimuthal quantum number.
For example, 1s is filled before 2s because 1s orbital is lower in energy as compared to 2s orbital.
The subshell ordering by this rule is: \[\;1s,{{ }}2s,{{ }}2p,{{ }}3s,{{ }}3p,{{ }}4s,{{ }}3d,{{ }}4p,{{ }}5s,{{ }}4d,{{ }}5p,{{ }}6s,{{ }}4f,{{ }}5d,{{ }}6p,{{ }}7s,{{ }}5f,{{ }}6d,{{ }}7p,{{ }}8s,{{ }}5g\] and so on.
But if this rule is not followed the ordering would be \[1s,{{ }}2s,{{ }}2p,{{ }}3s,{{ }}3p,{{ }}3d,{{ }}4s,{{ }}4p,{{ }}4d,{{ }}4f,{{ }}5s,{{ }}5p,{{ }}5d,{{ }}5f,{{ }}5g\] and so on.
In the question we are asked the atomic number of the first f-block element when Aufbau principle is not followed. The first element of f-block will have its outermost valence electron in 4f subshell Hence, we will start filling the subshells as:
\[1{s^2},{{ }}2{s^2},{{ }}2{p^6},{{ }}3{s^2},{{ }}3{p^6},{{ }}3{d^{10}},{{ }}4{s^2},{{ }}4{p^6},{{ }}4{d^{10}},{{ }}4{f^1}\] (when Aufbau principle is not followed)
Now by calculating the number of electrons, the atomic number (of the first f-block element when Aufbau rule is not followed) would be 47. But if Aufbau principle is followed the atomic number is 57.

So, the correct answer is Option B.

Note: The first f-block element will have \[4{f^1}\] configuration and hence only one electron in the f subshell. Any element with any number of electrons in \[4f\] subshell will not be considered as the first element of f-block.