Question

For a given value of $l$ , the total number of ' $m$ ' values are $2l + 1$ .
A True
B False

Answer 1

For a given value of $l$ , the total number of ' $m$ ' values represents the total number of sub energy levels in a given energy level. For example, a p orbital contains three degenerate ${p_x},{p_y},{p_z}$ orbitals. The four quantum numbers are the basis for a lot of chemical properties.

Complete Step by step answer: The symbol $l$ represents azimuthal quantum number.
The symbol $m$ represents a magnetic quantum number.
For a given value of $l$ , the total number of ' $m$ ' values are $2l + 1$ .
These include integer values from $- l$ to $+ l$ including zero.
For example, when $l = 0$ for an s orbital, $m$ can have only one possible value which is zero.
$2l + 1 = 2\left( 0 \right) + 1 = 1$
For a p orbital, $l = 1$, $m$ can have three possible values which are $- 1,0, + 1$ .
$2l + 1 = 2\left( 1 \right) + 1 = 3$
These correspond to ${p_x},{p_y},{p_z}$ orbitals.
For a d orbital, $l = 2$, $m$ can have five possible values which are $- 2, - 1,0, + 1, + 2$ .
$2l + 1 = 2\left( 2 \right) + 1 = 5$
These corresponds to ${d_{xy}},{d_{yz}},{d_{xz,}}{d_{{x^2} - {y^2}}},{d_{{z^2}}}$ orbitals.
For a f orbital, $l = 3$, $m$ can have seven possible values which are $- 3, - 2, - 1,0, + 1, + 2, + 3$ .
$2l + 1 = 2\left( 3 \right) + 1 = 7$
These correspond to seven f orbitals.

Hence, the given statement is true.

Additional information: For a given value of $n$ the total number of values of $l$ is equal to $n$ .

$n$ value	1	2	3	4
$l$ value	0	0,1	0,1,2	0,1,2,3
Number of $l$ value	1	2	3	4

Note: There are four quantum numbers that describe an electron in an atom. These are principal quantum number, azimuthal quantum number, magnetic quantum number and spin quantum number. Each one of them is having a significance and provides certain information about an atom and its shells ,subshells, orbitals and spin.