Question

calculate radial node angular node for 3d and 4f orbital​

Answer 1

Required Answer :-

(1) 3d

Principal quantum number = 3

Azimuthal quantum number = 2

• Angular nodes of a orbital is calculated by,

$\\ \star \: {\boxed{\purple{\sf{N_A = \: l }}}}$

Where ,

• $\sf{N_A}$ is angular nodes
• l is azimuthal quantum number

For 3d orbital , Azimuthal quantum number is 2. So , The number of angular nodes is also equal to 2.

• Radial nodes of a orbital is calculated by ,

$\\ \star \: {\boxed{\sf{\purple{N_R = n - l - 1}}}}$

Where ,

• $\sf{N_R}$ is number of radial nodes
• n is principal quantum number

For 3d orbital ,

• n = 3
• l = 2

→ $\sf{N_R}$ = 3 - 2 - 1

→ $\sf{N_R}$ = 0

Hence ,

• Number of radial and angular nodes for 3d orbital are 0 and 2

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(2) 4f

Principal quantum number (n) = 4

Azimuthal quantum number (l) = 3

For 4f orbital , Azimuthal quantum number is 3. So , The number of angular nodes is also equal to 3.

we have ,

• n = 4
• l = 3

Now applying the radial nodes formula ,

→ $\sf{N_R}$ = 4 - 3 - 1

→ $\sf{N_R}$ = 0

Hence ,

• The number of radial and angular nodes for 4f orbital are 3 and 0.