Question

Please explain this !!​

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Answer 1

Answer:

The azimuthal quantum number is a quantum number for an atomic orbital that determines its orbital angular momentum and describes the shape of the orbital. ... It is also known as the orbital angular momentum quantum number, orbital quantum number or second quantum number, and is symbolized as ℓ (pronounced ell).

Answer 2

Answered by @ItzHeartRider

$\quad \qquad { \sf { \huge { \mathfrak { \underbrace { \red { Azimuthal \: quantum \: number \: } } } } } }$

At first , you should note that Azimuthal quantum number is also known as Orbital Quantum Number or Subsidiary Quantum Number and it is denoted by the letter " ℓ "

• It helps us to find the Orbital Angular momentum of the given subshell .
• It helps us to determine the shape of the orbital .
• It's value is in the close interval [ 0 , ( n - 1) ] ( for only good explanation I take it in the close interval ) , here "n" represents number of subshell .

${ \sf { \huge { \mathfrak { \red { \underbrace {How \: to \: calculate \: ( ℓ ) :- } } } } } }$

As I told , It is calculated by the closed interval [ 0 , ( n - 1 ) ] where " n " = no. of subshell . Let's consider a example :-

1 . For subshell " s " :-

n = 1

ℓ = [ 0 , ( n - 1 ) ]

ℓ = [ 0 , ( 1 - 1 ) ]

ℓ = [ 0 , 0 ]

ℓ = 0

2 . For subshell " p " :-

n = 2

ℓ = [ 0 , ( n - 1 ) ]

ℓ = [ 0 , ( 2 - 1 ) ]

ℓ = [ 0 , 1 ]

ℓ = 0 , 1

3 . For subshell " d " :-

n = 3

ℓ = [ 0 , ( n - 1 ) ]

ℓ = [ 0 , ( 3 - 1 ) ]

ℓ = [ 0 , 2 ]

ℓ = 0 , 1 , 2

4 . For subshell " f " :-

n = 4

ℓ = [ 0 , ( n - 1 ) ]

ℓ = [ 0 , ( 4 - 1 ) ]

ℓ = [ 0 , 3 ]

ℓ = 0 , 1 , 2 , 3

${ \sf { \huge{ \mathfrak { \red { \underbrace { Shape \: of \: orbital :- } } } } } }$

For "ℓ = 0" ( s ) :-

• It's shape is spherical

For "ℓ = 1" ( p ) :-

• It's shape is dúmbbell

For "ℓ = 2" ( d ) :-

• It's shape is double dúmbbell

For "ℓ = 3" ( f ) :-

• It's shape is triple dúmbbell

And So on . . . . . . .

${ \sf { \huge { \mathfrak { \red { \underbrace {Orbital \: angular \: momentum :- } } } } } }$

It is calculated by a formula i.e ;

${ \sf { \sqrt{ ℓ × ( ℓ + 1 ) } × \dfrac{h}{2π} } }$

Here ,

• ℓ = Azimuthal Quantum Number
• h = planck constant

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