Question

How many nodes are there in the $1\mathrm{s},2\mathrm{p}$ and $3\mathrm{d}$ orbitals how many nodes are in a $4\mathrm{f}$ orbital?

Answer 1

The number of nodes in $1\mathrm{s},2\mathrm{p},3\mathrm{d}\mathrm{and}4\mathrm{f}$ orbitals:

Step 1: The number of node is related by principle quantum number($\mathrm{n}$) and azimuthal quantum number($\mathrm{l}$) .

Step 2:Formula used $\text{number of nodes= n-l-1}$.

Step 3: The number of nodes in $1\mathrm{s},2\mathrm{p},3\mathrm{d}\mathrm{and}4\mathrm{f}$ orbitals are given below:

• The number of nodes for $1\mathrm{s}$ orbitals

where, $\mathrm{n}=1$ and $\mathrm{l}=0$

The number of nodes $=\mathrm{n}-\mathrm{l}-1$

$$\begin{gathered} \mathrm{N}=1-0-1 \\ \mathrm{N}=0 \end{gathered}$$

• The number of nodes for $2\mathrm{p}$ orbitals,

where, $\mathrm{n}=2$ and $\mathrm{l}=1$

Number of nodes $=\mathrm{n}-\mathrm{l}-1$

$$\begin{gathered} \mathrm{N}=3-2-1 \\ \mathrm{N}=0 \end{gathered}$$

• The number of nodes for $3\mathrm{d}$ orbitals,

where, $\mathrm{n}=3$ and $\mathrm{l}=2$

Number of nodes $=\mathrm{n}-\mathrm{l}-1$

$$\begin{gathered} \mathrm{N}=3-2-1 \\ \mathrm{N}=0 \end{gathered}$$

• The number of nodes for $4\mathrm{f}$ orbitals

where, $\mathrm{n}=4$and $\mathrm{l}=3$

Number of nodes $=\mathrm{n}-\mathrm{l}-1$

$$\begin{gathered} \mathrm{N}=4-3-1 \\ \mathrm{N}=0 \end{gathered}$$

Thus, Zero nodes are present in $1\mathrm{s},2\mathrm{p},3\mathrm{d}$ and $4\mathrm{f}$ orbitals.