Question

calculate orbital angular momentum of last electron present in iron (z=26)​

Answer 1

To Find :

➳ Orbital angular momentum of last electron present in iron.

SoluTion :

⇒ Atomic number (Z) of Fe : 26

✴ Electronic configuration :

$\underline{\boxed{\bf{Fe(26) : [Ar]3d^6\:4s^2}}}$

⇒ Orbital angular momentum of electron is given by

$\bigstar\:\underline{\boxed{\bf{OAM=\sqrt{l(l+1)\:\dfrac{h}{2\pi}}}}}$

where, l denotes Azimuthal quantum number.

⇒ Principle quantum number (PQN) of last electron present in iron = 3

⇒ Azimuthal quantum number (AQN) of last electron present in iron = 2

(Because AQN of d orbital : 2)

$\longrightarrow\tt\:OAM=\sqrt{l(l+1)}\:\dfrac{h}{2\pi}\\ \\ \longrightarrow\tt\:OAM=\sqrt{2(2+1)}\:\dfrac{h}{2\pi}\\ \\ \longrightarrow\tt\:OAM=\sqrt{2(3)}\:\dfrac{h}{2\pi}\\ \\ \longrightarrow\underline{\boxed{\bf{OAM=\sqrt{6}\:\dfrac{h}{2\pi}}}}$

Learn More :

• AQN 'l' is also known as orbital angular momentum or subsidiary quantum number which defines the three dimensional shape of the orbital.

Answer 2

Orbital angular momentum of the last electron in iron:

Atomic number of Iron = 26.

$\boxed{ \sf{Fe \rightarrow \: 1 {s}^{2} 2 {s}^{2} 2 {p}^{6} 3 {s}^{2} 3{p}^{6} 4 {s}^{2} 3 {d}^{6} }}$

Arrangement of electrons in the 3d orbital:

$\boxed{ \sf{\{3d \} \rightarrow \{ \uparrow \downarrow\} \{\uparrow \} \{\uparrow \} \{\uparrow \} \{\uparrow \}}}$

So, the last electron is located in a "d" orbital with Azimuthal Quantum Number = 2.

Orbital angular momentum be P ;

$P = \sqrt{l(l + 1)} \: \hbar$

$= > P = \sqrt{2(2 + 1)} \: \hbar$

$= > P = \sqrt{2 \times 3} \: \hbar$

$= > P = \sqrt{6} \: \hbar$

So, final answer is:

$\boxed{ \red{ \huge{ \bold{ P = \sqrt{6} \: \hbar}}}}$