Question

What is the total no. of orbitals associated with the principal quantum number n=3?

Answer 1

Hint: The principal quantum number (n) describes the Orbital’s size. For example, orbitals for which n =3 are larger than those for which n = 2. As they have opposite electrical charges, electrons are attracted towards the nucleus of the atom. Energy is absorbed when an electron excites from an orbital in which the electron is close to the nucleus (n = 2) to an orbital in which it is further from the nucleus (n = 3). The principal quantum number, therefore, describes the energy of an orbital.

Complete step by step solution:

We generally describe the shell and subshell in which an orbital belongs by a two-character code; for example, 2p or 4f. The first character indicates the shell (n = 2 or n = 4) which we also call the principal quantum number. The second character identifies the subshell; for example, s, p, d and f.
The angular quantum number (l) describes the shape of the orbital. Orbitals have shapes which can be described as spherical (l = 0), polar (l = 1), or cloverleaf (l = 2). They can even have more complex shapes with an increase in the number of angular quantum numbers.
For s (l =0), p (l = 1), d (l = 2), f (l = 3)
There are nine orbitals in the n = 3 shell.
There is one orbital in the 3s subshell and three orbitals in the 3p subshell, n = 3 shell, also includes 3d orbitals.
There are three orbitals in the 3p subshell as there can be three directions in which p orbital can point. For example, one of these orbitals is oriented along the X axis, another along the Y axis, and the third along the Z axis of a coordinate system. These orbitals are known as the \[2{{p}_{x}}\], \[2{{p}_{y}}\], and \[2{{p}_{z}}\] orbitals.
For the 3d subshell there are five different orientations of orbitals, one of it lies in the XY plane of an XYZ coordinate system and it is called the 3dxy orbital. The \[3{{d}_{xz}}\] and \[3{{d}_{yz}}\] orbitals have the same shape, the only thing that they lie between the axes of the coordinate system in the XY and YZ planes. The fourth orbital in this subshell lies along the X and Y axes and is called the \[3{{d}_{{{x}_{2}}{{y}_{2}}}}\] orbital. The fifth orbital lies along the Z axis and this orbital is called the \[3{{d}_{{{z}_{2}}}}\] orbital.
The number of orbitals in a shell can be determined by squaring the principal quantum number. For example (n = 2) will have 2 $\times$ 2 = 4 orbitals.

Therefore, from the above statements we can conclude that the number of orbitals with the principal quantum number n = 3 are 9.

Note: We have two other quantum numbers namely:
Magnetic quantum number (m): It describes the orientation in space of a particular orbital.
Spin quantum number (s): Electrons behave as if they are spinning in either a clockwise or counterclockwise direction. One of the electrons in an orbital is assigned an s quantum number of +1/2, the other is assigned an s quantum number of -1/2.