Question

Calculate the total number of angular nodes and radial modes of 3p 4d and 4 s present in orbitals

Answer 1

$\huge {\bold {\underline {\underline {Given : - }}}}$

• Orbitals are 3p , 4d , 4s

$\huge {\bold {\underline {\underline{To \: find : - }}}}$

• Total number of Angular and radial nodes of orbitals 3p , 4d , 4s

$\huge {\bold {\underline {\underline{Solution : - }}}}$

Number of Angular nodes of the orbital is given by ,

$\large {\bold {\boxed{ \bigstar{ | {N}_{A} = l | }}}}$

Where ,

• l is azimuthal quantum number

Number of radial nodes of the orbital is given by ,

$\large {\bold {\boxed{ \bigstar{ | {N}_{R} = n - l - 1 | }}}}$

Where ,

• n is principal quantum number
• l is azimuthal quantum number

Fist let us calculate the angular and Radial nodes for ,

• 3d
• 4d
• 4s

i] 3d

a) Number of angular nodes

l value of 3d = 2

∴ Number of angular nodes for 3d-subshell is 2

b) Number of Radial nodes

n- Value for 3d subshell = 3

l - value for 3d subshell = 2

Number of radial nodes = 3 - 2 - 1 = 0

∴ Number of radial nodes for 3d subshell is 0

ii] 4d

a) Number of angular nodes

l - value for 4d orbital = 2

∴ Number of angular nodes for 4d subshell is 2

b) Number of radial nodes

n-value for 4d orbital = 4

l - value for 4d orbital = 2

∴ Number of radial nodes for 4d subshell = 4 - 2 - 1 = 3

iii] 4s

a) Number of angular nodes

l - value for 4s subshell = 0

∴ Number of angular nodes for 4s subshell = 0

b) Number of radial nodes

n - value for 4s subshell = 4

l - Value for 4s subshell = 0

∴ Number of radial nodes for 4s subshell = 4 - 0 - 1 = 3

Answer 2

Answer:

\huge {\bold {\underline {\underline {Given : - }}}}

Given:−

Orbitals are 3p , 4d , 4s

\huge {\bold {\underline {\underline{To \: find : - }}}}

Tofind:−

Total number of Angular and radial nodes of orbitals 3p , 4d , 4s

\huge {\bold {\underline {\underline{Solution : - }}}}

Solution:−

Number of Angular nodes of the orbital is given by ,

\large {\bold {\boxed{ \bigstar{ | {N}_{A} = l | }}}}

★∣N

A

=l∣

Where ,

l is azimuthal quantum number

Number of radial nodes of the orbital is given by ,

\large {\bold {\boxed{ \bigstar{ | {N}_{R} = n - l - 1 | }}}}

★∣N

R

=n−l−1∣

Where ,

n is principal quantum number

l is azimuthal quantum number

Fist let us calculate the angular and Radial nodes for ,

3d

4d

4s

i] 3d

a) Number of angular nodes

l value of 3d = 2

∴ Number of angular nodes for 3d-subshell is 2

b) Number of Radial nodes

n- Value for 3d subshell = 3

l - value for 3d subshell = 2

Number of radial nodes = 3 - 2 - 1 = 0

∴ Number of radial nodes for 3d subshell is 0

ii] 4d

a) Number of angular nodes

l - value for 4d orbital = 2

∴ Number of angular nodes for 4d subshell is 2

b) Number of radial nodes

n-value for 4d orbital = 4

l - value for 4d orbital = 2

∴ Number of radial nodes for 4d subshell = 4 - 2 - 1 = 3

iii] 4s

a) Number of angular nodes

l - value for 4s subshell = 0

∴ Number of angular nodes for 4s subshell = 0

b) Number of radial nodes

n - value for 4s subshell = 4

l - Value for 4s subshell = 0

∴ Number of radial nodes for 4s subshell = 4 - 0 - 1 = 3