Question

In any subshell, the maximum numbers electrons having the same value of Quantum number is:
(This question has multiple correct options)
A.$\sqrt {l(l + 1)} $
B.$l + 2$
C.$2l + 1$
D.$4l + 2$

Answer 1

Hint:Three-dimensional areas of space which have the most probability of electrons is called an atomic orbital. An orbital has a maximum 2 electrons of opposite spin quantum. It means in any subshell, the maximum number of electrons having the same value of the spin quantum number is equal to the number of orbitals.

Complete step by step answer:
2L + 1 is the correct answer.
On the basis of shape, there are four types of an atomic orbital.
S- orbital = Spherical
P- orbital = Dumb bell-shaped
D - orbital = Double dumbbell shaped
f - orbital = Complicated
A subshell is denoted by its azimuthal quantum number L. The value of azimuthal quantum number l is g represented by s, p, d, f.

Subshell	s	p	d	f
L	0	1	2	3

Value of l depends on the principal quantum number n. for any n, l has value 0 to(n-1).
For any n, the total number of l is equal to n.
For example:-
n=1 , No. of l =1 (1s)
n=2, number of l = 2 (2s, 2p)
n=3, number of l =3 (3s, 3p, 3d)
L- azimuthal quantum number is also called orbital quantum number. spin quantum number denotes the two spin states of an electron. Direction of spin of the electron may be clockwise or anticlockwise. For any quantum number m, spin quantum has two values 1/2, and -1/2 .
Spin quantum number represented by S.
Magnetic quantum number m depends on the azimuthal quantum number l. for any l, m has value +l to - l including zero.
For example
L=0 then m=0
L = 1 then m = +1 ,0 , -1
L = 2 then m = +2, +1, 0, -1, -2

Note:
For any l, total number of $m = 2l + 1$
Total number of orbits in any subshell is $2l + 1$ and one orbital has two electrons of opposite spin. Maximum number of electrons in any subshell is $2(2l + 1) = 4l + 2$ but they are not in the same spin.
Number of electrons having the same value of spin quantum number is $2l + 1$.
For example
l =0 (s subshell)
total number of electrons = 2
Number of orbital = 1 ${\boxed{ \uparrow \downarrow }_{\dfrac{1}{2}}}^{^{\dfrac{{ - 1}}{2}}}s$
 l = 1 ( p subshell)
number of orbitals = $2l + 1$ = 2+1 = 3.
Total number of electrons = 2× 3 = 6.
$\boxed{ \uparrow \downarrow }\boxed{ \uparrow \downarrow }\boxed{ \uparrow \downarrow }$
Number of electrons of the same spin is equal to no of orbitals . In this, the number of electrons of the same spin is 3.