Consider the ground state of Cr atom (Z = 24). The numbers of electrons with the azimuthal quantum numbers, l = 1 and 2 are, respectively:

The correct option is 12 and 5.

To find the number of electrons with azimuthal quantum numbers
$l=1$
and
$l=2$
in a ground-state Chromium (Cr) atom, we follow these systematic steps:

Step 1: Write the electronic configuration of Chromium (Z = 24)
Chromium is a well-known transition metal that exhibits an exception to the standard Aufbau principle. Due to the extra thermodynamic stability associated with a half-filled
$d$
subshell, one electron from the
$4s$
orbital is promoted to the
$3d$
orbital. Therefore, the ground-state electronic configuration of Chromium (atomic number
$Z=24$
) is:
$1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}3d^{5}4s^1$

Step 2: Understand the azimuthal quantum number ($l$)
The azimuthal quantum number (
$l$
) determines the shape of the orbital and identifies the subshell:
- For $s$-orbitals: $l=0$
- For $p$-orbitals: $l=1$
- For $d$-orbitals: $l=2$

Step 3: Count the electrons with $l=1$ (p-orbitals)
The subshells corresponding to
$l=1$
are the
$p$
subshells. Looking at Chromium's ground-state configuration:
- The
$2p$
subshell contains 6 electrons ($2p^6$).
- The
$3p$
subshell contains 6 electrons ($3p^6$).
Adding these together:
$6+6=12$
So, there are 12 electrons with azimuthal quantum number
$l=1$
.

Step 4: Count the electrons with $l=2$ (d-orbitals)
The subshell corresponding to
$l=2$
is the
$d$
subshell. Looking at Chromium's ground-state configuration:
- The
$3d$
subshell contains 5 electrons ($3d^5$).
So, there are 5 electrons with azimuthal quantum number
$l=2$
.

Conclusion:
The numbers of electrons with azimuthal quantum numbers
$l=1$
and
$l=2$
are 12 and 5, respectively.