Question

How would you find how many orbitals a sublevel has?

Answer 1

To answer this question we should know about quantum numbers n, l, ml and ms. We should know which quantum number represents the sublevel. Each energy level contains sublevel. These sublevels contain orbitals. In which electrons get filled.

Complete step by step answer:
Electronic configuration of an atom has four quantum numbers. n, l, ml and ms.
L is known as azimuthal quantum number.
Azimuthal quantum number: it tells the sublevel and shape of the orbital.
Its value ranges from $0 - ({\text{n}} - 1)$.
The name of orbital is given by numbers which are shown as follows:

Number	sublevel name
$0$	s
$1$	p
$2$	d
$3$	f

The formula to calculate the number of orbital in a sublevel is as follows:
${\text{2l}}\,{\text{ + }}\,{\text{1}}$

So, the number of orbitals in each sublevel is shown as follows:

Number	sublevel name	${\text{2l}}\,{\text{ + }}\,{\text{1}}$	Number of orbital
$0$	s	${\text{2}} \times \,{\text{0}}\,{\text{ + }}\,{\text{1}}$	$1$
$1$	p	${\text{2}} \times \,1\,{\text{ + }}\,{\text{1}}$	$3$
$2$	d	${\text{2}} \times \,2\,{\text{ + }}\,{\text{1}}$	$5$
$3$	f	${\text{2}} \times \,3\,{\text{ + }}\,{\text{1}}$	$7$

Therefore, we would find the orbitals a sublevel has by using the ${\text{2l}}\,{\text{ + }}\,{\text{1}}$ formula.

Additional information:
Principle quantum number: it tells the energy level or shell.
Its value ranges from $1 - \infty$.
The name of energy level is given by alphabets which are shown as follows:

Energy level	Name of the level
$1$	K
$2$	L
$3$	M
$4$	N

Magnetic quantum number: It tells the orbital of the subshell.
Its value ranges from $( - {\text{l)}}\, - ({\text{ + l}})$.
It is determined by ${\text{2l}}\,{\text{ + }}\,{\text{1}}$.
Spin quantum number: It tells the spin of an electron. Its value is $\dfrac{- 1}{2}$ or $\dfrac{+ 1}{2}$.

Note: s-orbital is spherical in shape and contains one-orbital. P-orbital is dumbbell in shape. D-orbital sis double dumble in shape. F-orbitals are complex in shape. The maximum number of electrons gained by s-orbital is two. The maximum number of electrons gained by p-orbital is six. The maximum number of electrons gained by d-orbital is ten. The maximum number of electrons gained by f-orbital is fourteen.