### What are the atomic orbitals?

- A wave function represents an electron is the product of two parts, a radial part, and an angular part.

- The square of the radial part of the wave function indicates the probability of finding the electron at any distance r from the nucleus.

- The square of the angular part of the wave function gives the probability of finding an electron in a particular direction from the nucleus.

- The radial dependence and angular dependence of wave function taken together, tell us that a three-dimensional standing electron wave (orbital) can be a picture to have size, shape, and orientation of an orbital.

- In order to describe the size, shape, orientation of an orbital four quantum numbers are necessary. These quantum numbers are designed as,

- Principal quantum number
- Azimuthal quantum number
- Magnetic quantum number
- Spin quantum number

#### Principal quantum number of an atom

- The principal quantum number(n) is of primary importance in determining the size and hence the energy of an electron.

- Hydrogen, the energy is fixed by the value of the principal

**quantum number**(n). In other multi-electron atoms, the energy of each electron depends on the value of the principal quantum number of the electron.

- As the value of the principal quantum number(n) increases the radius (the nucleus of an atom and electron separation increases that are the size of the orbital increases).

- The energy also raised, principal quantum numbers(n) is always an integer and can assume the value,1,2,3,4.... but not zero.

#### Azimuthal quantum number of an atom

- The general geometric shapes of an electron wave or orbital are described by the azimuthal quantum number. This quantum number related to the electron in that state.

Thus, l = 0, 1, 2, 3.....(n-1)

- Therefore an electron having principal quantum number n, assumed the values l is 0 to (n-1).

#### Magnetic quantum number of an atom

- The magnetic quantum number associated with the orientation of the electron wave with respect to a given direction, usually that of a strong magnetic field. This quantum number hasn't an effect on the shape of orbital or on the energy of an electron.

For a given value of l, ml can have any integral value between +1 to -1.

∴ m

∴ m

_{l}= + l, (l - 1), (l - 2), (l - 3) ..... 0 ..... - 1, - 2, - l#### Spin quantum number of an atom

- Besides the three quantum numbers, it also has a fourth quantum number namely spin quantum number (s), which was necessary to completely describe an electron in a particular shell.

- The electron itself regarded as a small magnet. A beam of a hydrogen atom can be split into two beams by a strong magnetic field. This indicates that there are two kinds of the hydrogen atom in which can be differentiated on the basis of their behavior in a magnetic field.

- It has been postulated that each electron spin around its axis like a lope and they behave like a magnet. A spinning electron can have only two possibilities.

- The electron can either spin clockwise or counterclockwise. The two directions of spin represent as(↑↓).

- This four quantum number s = 1/2 is independent of the other three quantum numbers.

- Two directions of spin are represented as (↑↓) can have two possible ms values +1/2 and -1/2 depending on the direction of rotation of the electron about its axis.

#### How to find the quantum numbers of orbitals?

Quantum energy levels of an atom |

- What are the four quantum numbers of the 19th electron of chromium?

- The atomic number of chromium is 24. Thus the electronic configuration of chromium is,

1S² 2S² 2P⁶ 3S² 3P⁶ 4S¹ 3d⁵

- 19th electron means 4S¹ electron. Thus for 4S electron n =4, and l =0 and for S¹ electron m = 0 and s = +½.

∴ The four quantum numbers of the 19th electron of chromium are

4, 0, 0, +½

Question4, 0, 0, +½

- Write the correct set of four quantum numbers for the valence electron of rubidium.

- The correct set of four quantum numbers for the valence electron of rubidium atom are,

5, 0, 0, +½

Question- How many electrons in an atom can have the following quantum numbers n=4 and l=1?

- 6 electrons in an atom can have the following quantum numbers n =4 and l =1.

- How many possible orbitals are there for n = 4?

Thus the number of possible orbitals when

n = 4 is [1(4S) + 3(4P) + 5(4d) + 7(4f)] = 16

Questionn = 4 is [1(4S) + 3(4P) + 5(4d) + 7(4f)] = 16

- How many possible orbitals are there for n = 3, l =1, and m

_{l}=0 ?

- Thus the number of orbitals is 1, 3S orbital.

### What are atomic orbitals? and S, P, d subshell

- An orbital is a region in space where there is a high probability of finding an electron.

- The S orbitals penetrate the nucleus most while the P and d subshell cannot penetrate the nucleus.

- This means that S orbital electron can efficiently screen the nuclear charge from other electrons compared to the other P and d electrons.

- The wave function of the electron in an atom is called orbital. The wave function is plotted against distance and space in three dimensional marked by a curve will give the shape of the orbitals.

- The probability of finding an electron in space around the nucleus involves two aspects, radial probability, and angular probability.

- It is not possible to represent completely in one diagram on paper the directional properties of electron orbitals. An angular probability distribution must be combined mentally to have an overall shape of the orbital.

#### Orbital electron distribution in s sublevel

- The angular probability distribution is greater interest and importance, an S orbital electron has no angular dependence because the relevant wave function is independent of angles Î¸ and Î¦.

- There is, therefore, an equal chance of discovering the electron in any direction of the nucleus.

S subshell of an atom |

- With the nucleus at the origin of the Cartesian axes, the sphere of the radius(r) represents the probability of finding the electron in S orbital.

- An S orbital electron has a spherically symmetrical probability distribution.

#### Shape of P subshell of an atom

- The P orbitals are three orientations is represents as, Px, Py, and Pz. The orientations of the orbital plane correspond to ml = 1, 0, -1 is mutually at the right angles.

- So the orbitals designated Px, Py and Pz are mutually perpendicular and they are concentrated along the respective coordinate axis X, Y and Z. Unlike the S orbitals, the angular part of the P wave function is dependent on Î¸ and Î¦.

P subshell of an atom |

#### Shape of d-subshell of an atom

- These orbital arises when n =3 (M - shell), that is the orbitals start with the 3rd main energy level.

When l = 2(d - orbital),

m = -2, -1, 0, 2, 1

indicating that d - orbitals have five orientation, that is,

dxy, dxz, dyz, dx² - y² and dz²

m = -2, -1, 0, 2, 1

indicating that d - orbitals have five orientation, that is,

dxy, dxz, dyz, dx² - y² and dz²

- All these five d - orbitals, in the absence of a magnetic field, are equivalent in energy and are, therefore, said to be five-fold degenerate.

d subshell of an atom |