Question

The total number of atomic orbitals in the fourth energy level of an atom is?
A.4
B.8
C.16
D.32

Answer 1

Hint: In a shell, there are subshells. The principal quantum number gives the number of shells in an atom. The principal quantum number is denoted by n. Principal quantum numbers can have integer values that can be positive or greater than one. It denotes the energy levels.

Complete step by step answer:
In the question, it is asked to find out the total number of atomic orbitals in the fourth energy level of an atom.
We know about the principal quantum number, n.
It describes the most probable distance between the nucleus and the electrons.
If the principal quantum number is larger, then the distance between the nucleus and the electrons is larger and thus it implies a greater atomic size.
The principal quantum number can never be negative.
If the principal quantum number value, n is 1, then it denotes the lowest energy state or ground state.
Here in the question, we have to consider the fourth energy level of the atom. So here the value of the principal quantum number, n is 4.
Thus here we have to consider the fourth shell.
The question is to find out the total number of atomic orbital in the fourth shell whose n value is 4. We know the formula to find out the number of atomic orbitals is ${n^2}$.
Here the energy level, $n = 4$.
Therefore the total number of atomic orbitals in the fourth energy level is ${n^2} = {4^2} = 16$.
Thus the total number of atomic orbitals in the fourth energy level of an atom is 16.
Here the answer is an option (C).

Note:
Total number of atomic orbitals in an energy level n is given by ${n^2}$ . In ${n^{th}}$ energy level, there are n subshells. Thus in the ${4^{th}}$ shell there are 4 subshells s,p,d, and f. For subshells there is one orbital. For subshell p there are 3 orbitals. For subshell d there are five orbits and then for f orbital, there are seven orbitals. Thus total $1 + 3 + 5 + 7 = 16$ orbitals.