To answer the question we must first identify what is the electronic configuration of each element. The electronic configuration indicates the way in which the electrons are arranged in the different energy levels. The following scheme shows us how the different levels of energy are filled.
Source: "https://commons.wikimedia.org/wiki/File:Diagrama_de_Configuraci%C3%B3n_electr%C3%B3nica.svg"
Each level is capable of storing a certain amount of electrons.
s = 2 electrons
p = 6 electrons
d = 10 electrons
f = 14 electrons
Now, let's see how many electrons each element has and what its electronic configuration will be.
Fe:26 electrons
Electronic configuration
[tex]1s^22s^22p^63s^23p^64s^23d^6[/tex]
There is no "f" orbital in Fe
Au: 79 Electrons
Electronic configuration
[tex]1s^22s^22p^63s^23p^63d^{10}4s^24p^64d^{10}5s^25p^64f^{14}5d^{10}6s^1[/tex]
In this element,"f" orbital is in the 4th level of energy
Ba: 56
Electronic configuration
[tex]1s^22s^22p^63s^23p^63d^{10}4s^24p^64d^{10}5s^25p^66s^2[/tex]
We do not have "f" orbital here in Ba
Es: 99
Electronic configuration
[tex]\lbrack Rn\rbrack5f^{11}7s^2[/tex]
That is an abbreviation of the electronic configuration. We have that Es have an "f" orbital in the 5th level of energy.
C: 12
Has 12 electrons, less than Au and Ba. So this element does not have an f orbital.
The answer will be then: Es
