Question

From the diagrams of $\mathbf{2}\mathit{p}\mathbf{,}\mathbf{3}\mathit{p}\mathbf{-}$orbitals in Fig. 12.9 and Fig. 12.10 , respectively, draw a rough graph of the square of the wave function for these orbitals in the direction of one of the lobes.

Short answer

Areas of zero probability of finding an electron are also called nodes or nodal surfaces.

The number of nodes is given by$(n-l-1)$ .

Step-by-step solution

Explain the concept of nodes:

Areas of zero probability of finding an electron are also called nodes or nodal surfaces.

The number of nodes is given by$(n-l-1)$ .

Now consider the signs of the mathematical function:

$p_z$ orbital has a positive sign in every region of space where z is a positive and a negative sign when z is negative. 3p- orbitals have a more complex probability distribution than 2p.

Apply these concepts to plot the graph between |ψ|2 and r :

For $2p$, number of nodes$=n-l-1=2-1-1=0$

For $3p$, number of nodes $=n-l-1=3-1-1=1$

So there will be no node in the probability distribution of $2p$ while $3p$will have 1 node.

Number of peaks is given by$(n-l)$

Therefore peaks in$2p=2-1=1$

and in$3p=3-1=2$