Question

How many nodal planes are there in the atomic orbitals for the principal quantum number n=3 ?
A. 10
B. 9
C. 11
D. 2

Answer 1

Hint: Nodal plane is a plane that passes through a nucleus where the probability of finding an electron is almost zero. The number of nodal planes for any orbital is equal to azimuthal quantum number is denoted by “l”.

Complete step by step answer:

- Now, the shell whose principal quantum number is 3, the value of l possible are:
n=3, number of subshell is $l=0\text{ }to\text{ }\left( n-1 \right)$
\[\begin{align}
  & l=0\text{ }to\text{ }\left( 3-1 \right) \\
 & l=0\text{ }to\text{ }\left( 2 \right) \\
 & l=0\text{ }to\text{ }2 \\
\end{align}\]

- We can see that value of l possible are 0, 1, 2, so we can say that 3s , 3p, 3d subshell will be present, out of which there is one orbital present in 3s subshell, 3 orbitals present in 3p subshell that are $\left( 3{{p}_{x}},3{{p}_{y}},3{{p}_{z}} \right)$ and 5 orbitals present in 3d subshell that are $\left( 3{{d}_{xy}},3{{d}_{yz}},3{{d}_{zx}},3{{d}_{{{x}^{2}}-{{y}^{2}}}},3{{d}_{{{z}^{2}}}} \right)$.

- In general, we can say that the number of nodal planes for any orbital is the Azimuthal quantum number (that is denoted by l) of that orbital.

- We can say that, in 3s subshell there is zero nodal plane. In 3p subshell there will be three nodal planes, one from each $\left( 3{{p}_{x}},3{{p}_{y}},3{{p}_{z}} \right)$.

- In 3d , there will be 8 nodal planes, 2 from each $\left( 3{{d}_{xy}},3{{d}_{yz}},3{{d}_{zx}},3{{d}_{{{x}^{2}}-{{y}^{2}}}} \right)$ and there are zero nodal plane in $3{{d}_{{{z}^{2}}}}$this is an exception .

- So, we can write the total nodal planes of the atomic orbitals for the principal quantum number n = 3 as: 0 + 3 + 8 = 11

Hence, we can conclude that the correct option is (C) that 11 nodal planes are there in the atomic orbitals for the principal quantum number n = 3.

Note:

-Nodal planes and Nodal surfaces are different. As we know the number of nodal planes for the orbital is denoted by the value of ‘l’ but in case of nodal surface, the number of nodal surfaces can be determined by the n-l-1 where n = principal quantum number and l = azimuthal quantum number.
- Nodal planes are also called angular nodes while nodal surfaces are also known as radial nodes.
- There are zero nodal planes in $3{{d}_{{{z}^{2}}}}$, this is an exception.