Question

For a given l value, the total number of m values are,
A) $2l + 1$
B) $l + 1$
C) $2l + 2$
D) $2l - 1$

Answer 1

Hint: We know the principal energy level of an electron denotes the orbital in which the electron is situated according to the atom’s nucleus. The Azimuthal quantum number represents the subshell to which the electron is present and also tells us the shape of the orbital and the energy associated with the angular momentum of the electron. The chosen orientations of orbitals in space determined by magnetic quantum number.
The spin quantum number’ is related to electron spin.

Complete step by step answer:
We know that,
The principal quantum number is denoted by n. The value of shell ‘$K$’ has been given $n=1$, the ‘$L$’ shell has been given the value $n=2$. The secondary quantum number l divides the shells up into smaller groups of subshells and orbitals.
${\text{Value of }}'l':0,1,2,3$
${\text{Letter designation}}:s,p,d,f$
Energy of an orbital is governed by \[n + l\] value where n=principal quantum number and l=Azimuthal quantum number. For \[2s\] orbital \[n + l = 2 + 0 = 2\] and for \[2p\] it is\[2 + 1 = 3\] , and since \[n + l\] value is lower for \[2s\] orbital then, its energy will be lower than that of \[2p\] -orbital.
Magnetic Quantum Number: It portrays the direction of the orbitals. It is spoken to as $m$ . The estimation of this quantum number reaches from $ - l$ to $ + l$. The sum of magnetic quantum numbers is $2l + 1$.
Hence option A is correct.

Note:
-As indicated by Pauli's avoidance standard: The two electrons present in any orbital have turn quantum numbers with a contrary sign \[{m_s} = + 1/2\] and $ - 1/2$ .
-The state of a nuclear orbital is dictated by the precise energy quantum number which is otherwise called Azimuthal quantum number assigned by "l". The diverse shapes of orbitals are also known as,
$l = 0 \to s - orbital$
$l = 1 \to p - orbital$
$l = 2 \to d - orbital$
$l = 3 \to f - orbital$.