Question

Consider the ground state of $Cr$ atom $\left( Z\text{ }=\text{ }24 \right).$ The numbers of electrons with the azimuthal quantum numbers, $l\text{ }=\text{ }1$ and $2$ are, respectively:

Answer 1

We know that quantum number is a set of numbers with the help of which we can locate the position of an electron in an atom. There are four quantum numbers in total and using them we can calculate the number of electrons in a shell and subshell of an element.

Complete answer:
We all know that there are four quantum numbers including: Principal quantum number tells us about the size of the electron cloud and energy level of the electron and is represented by $n.$ The shells $K,\text{ }L,\text{ }M,\text{ }N,\text{ }O,\text{ }P$ have the $n=1,2,3,4,5,6~$ respectively. The azimuthal quantum number tells us about the shape of electron could and subshell to which the electron belongs, represented as $l$ and subshells $s,\text{ }p,\text{ }d,\text{ }f,\text{ }g$ have $l=0,1,2,3,4~$ respectively.
The magnetic quantum number tells us about the orientation of the electron cloud, represented by $m$ and for a given value of $l,\text{ }m$ can be $l$ to $0$ to $+l$ and finally the spin quantum number which tells about the spin or rotation of the electron in its own axis. The electronic configuration of $Cr$ along with the values of the quantum numbers $n$ and $l$ are shown.

| $n$ | $1$
---|---|---
$1{{s}^{2}}$ | $1$ | $0$
$2{{s}^{2}}$ | $2$ | $0$
$2{{p}^{6}}$ | $2$ | $1$
$3{{s}^{2}}$ | $3$ | $0$
$3{{p}^{6}}$ | $3$ | $1$
$3{{d}^{5}}$ | $3$ | $2$
$4{{s}^{1}}$ | $4$ | $0$

Thus the number of electrons with $l=1$ is $12$ and the number of electrons with $l=2$ is $5.$
Therefore, the correct answer is $12$ and $5$ respectively.

Note:
Remember that the probability of finding an electron is said to be zero in case of radial nodes. Angular nodes are equal to the value of azimuthal quantum number, and since the value for azimuthal quantum number for d orbital is two, the value for angular nodes also has to be two. The number of nodes increases when the principal quantum number increases.