Question

Which of the following has highest orbital angular momentum?
A. \[4s\]
B. $4p$
C. $4d$
D. $4f$

Answer 1

Hint:Each of the specific orbitals have different spins of electrons and the quantum number varies for different orbitals and respective electrons. Here the angular momentum needs to be understood using the specific quantum value for the given orbitals.

Complete step-by-step answer:Determining the orbital angular momentum depends on the azimuthal quantum number of the specific orbital choices that are given here. The azimuthal quantum number is defined by $l$. The value of $l$ for $4s$ is $0$, for $4p$ is $1$, for $4d$ is $2$, for $4f$ is $3$. The calculation of specific orbital angular momentum depends on the specific formula for angular momentum for the specific orbital with azimuthal quantum values. The formula that is chosen for this purpose is: ${\mu _l} = \sqrt {l\left( {l + 1} \right)} \dfrac{h}{{2\pi }}$
In this the $l$ is the azimuthal quantum number, ${\mu _l}$is the orbital angular momentum for the given orbital. The $h$ is the Planck’s constant in the given equation. Therefore, the only variable in the whole equation for determining the orbital angular momentum is the azimuthal quantum number $\left( l \right)$. According to the given formula, the higher value of the azimuthal quantum number shows a higher value of the orbital angular momentum. Based on this formula, the one orbital with the highest orbital angular momentum is $4f$ as the value of $l$ or the azimuthal quantum number for the specific orbital is $3$.

Hence the correct option is (B).

Note:The angular momentum in the orbital is associated with the velocity of the electrons residing in the electrons. The given results suggest that the electrons of different spin can have a specific moment as it resides in the specific orbital.