Question

The atom cobalt has 27 electrons. How many energy levels will its electrons use?

Answer 1

Hint: We know that energy levels are also known as electron shells like K shell, L shell etc. These shells are fixed distances from the nucleus where electrons are found. The number of electrons in an energy level can be calculated by the formula, Number of electrons=$2{n^2}$, where n represents the number of the energy level.

Complete step by step answer:
Let’s understand how to calculate the number of electrons using the formula $2{n^2}$.
For the 1st shell, n=1
No. of electrons present in 1st shell=$2{n^2} = 2$
For the 2nd shell, n=2
No. of electrons present in 2nd shell=$2{n^2} = 2 \times {2^2} = 8$
For the 3rd shell, n=3
No. of electrons present in 3rd shell=$2{n^2} = 2 \times {3^2} = 18$
Now, come to the question. We have to identify the number of energy levels of Cobalt. We know that there are four subshells in an energy level, that is, s,p, d and f. Electrons are present in these subshells.

In the first shell, n=1 and there is only one subshell, that is, 1s
In the second shell, n=2 and there is two subshell, that is, 2s and 2p
In the third shell, n=3 and there is three subshell, that is, 3s, 3p and 3d
In the fourth shell, n=4 and there is four subshell, that is, 4s, 4p, 4d and 4f
While assigning electrons to each subshell we have to follow the Aufbau principle and each subshell can maximum contain two electrons.
In the case of cobalt there are 27 electrons to be filled. And we know that the energy of the 4s energy level is less than the 3d energy level. So, electrons fill first in 4s and then in 3d. So, the electron configuration of Cobalt is,
$1{s^2}2{s^2}2{p^6}3{s^2}3{p^6}4{s^2}3{d^7}$
So, we find that 1st energy level contains 2 electrons
2nd energy level contains 8 electrons
3rd energy level contains 15 electrons
4th energy level contains 2 electrons

So, the number of energy levels needed by a cobalt atom is 4.

Note: It is to be noted that Aufbau principle states that while filling electrons in a subshell of an atom, the subshell that has less energy is to be filled first than the higher energy subshells. The increasing order of energies of various orbitals is:
1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 4d, 5p……