## Quantum Numbers Orbital Diagram

**Quantum numbers** set like principal, azimuthal, magnetic, and spin **quantum** number and fine structure of electromagnetic spectrum lines of atoms in quantum mechanics define the electron energy levels and shapes diagram of s, p, d-**orbital** or **orbitals** in physics and chemistry. Bohr’s theory of hydrogen spectrum and Sommerfield theory met with difficulties when these theories applied for characteristics of ply-electronic atoms. Therefore, in learning chemistry, principal, azimuthal, magnetic, and spin quantum number set very useful for identifying the special lines and diagram shapes of s, p, d, and f orbitals of chemical elements in presence in the periodic table.

For the study the fine structure of atoms four quantum number needed to explain the various absorption or emission spectrum of photon particle. These numbers are the identification numbers for individual electron particles in an atom to describe the position and energy level of an atom. In order to study the size, shapes, the orientation of orbitals principal, azimuthal, magnetic, and spin quantum numbers are necessary.

### Identify the Principal Quantum Number

The principal quantum number describes the set of energy levels or the principal shell in quantum mechanics to which an electron can stay denoted by n. Hence the primary importance of the principal quantum number for determining the size of an atom and energy of an electron. From Bohr’s theory of the hydrogen, the energy set of the hydrogen energy levels fixed in the fixed value of n.

But the energy value of each electron depends mostly on the n of an orbital in quantum mechanics. As the value of the n increases the atomic radius or nucleus electron separation increases and the energy also raised. The n always an integer and can assume the value, n = 1, 2, 3, 4…. but not zero.

### Azimuthal Quantum Number

The azimuthal quantum number was introduced by Sommerfeld in his atomic model and gives the angular momentum of an electron in its elliptical movement around the nucleus of an atom and the fine structure of the emission spectrum. Therefore, the general geometric shapes of an electron cloud or orbitals define by the azimuthal quantum number or angular momentum quantum number. Permitted values of l for a given value of n has 0 to (n-1).

∴ l = 0, 1, 2, 3…..(n-1)

The total number of different values of l equal to n.

n = 1, l = 0 (1s-orbital)

For 2s and 2p-orbital, n = 2, l = 0, 1

n = 3, l = 0, 1, 2 (3s, 3p, and 3d-orbital)

### Magnetic Quantum Number

Bohr’s model hydrogen could not explain the splitting of a single spectral line into a number of closely spaced lines in presence of magnetic field or presence of the electric field. Thus the presence of more lines in the spectrum of the magnetic field or electric field indicates the electron energy levels are further subdivided by the additional set of numbers called magnetic quantum number.

The magnetic quantum number identifies the orientation of shapes of electron clouds with respect to a given direction, usually that of a strong magnetic field. This denoted by m_{l}. For a given value of the azimuthal quantum number, the magnetic quantum number can have any integral value between +1 to -1.

### Spin Quantum Number in Physics

When spectral lines of hydrogen, lithium, sodium, and potassium observed by the instrument of high resolving power, each of the lines of the spectral series was found to consist of a pair of lines known double line structure. Therefore, to identify these double lines of the fine structure another fourth number necessary, and it is known as a spin quantum number. But the electron itself regarded as a small magnet. A beam of the hydrogen spectrum can split into two beams by a strong magnetic field.

This indicates that there are two kinds of spin that can be differentiated on the basis of their environment in a magnetic field. Hence the electron has either spin clockwise or counterclockwise. The spin quantum number independent of the other three numbers. Because two directions of spin have two possible spin values (+ ½) and (- ½). Therefore, these values depending on the direction of rotation of the axis of the electron.

### Calculate Quantum Numbers of the Atom

Question**: **What are the four quantum numbers of the 19th electron of chromium in the periodic table?

Answer: The atomic number of chromium 24. Thus the electron configuration of chromium, 1s^{2} 2s^{2} 2p^{6} 3s^{2} 3p^{6} 4s^{1} 3d^{5}. Hence 19th electron means 4s^{1} electron and the quantum number for this electron, n = 4, l = 0, m = 0, and s = +½.

Question: Find out the correct set of four quantum numbers for the valence electron of rubidium.

Answer: The correct set of four quantum numbers for the valence electron of the rubidium atom, 5, 0, 0, +½.

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

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

Question: How many possible numbers of orbitals of an atom when n = 4?

Answer: Number of possible orbitals when n = 4, [1 (4s) + 3 (4p) + 5 (4d) + 7 (4f)] = 16.

Question: How many possible orbitals are there when n = 3, l = 1, and m_{l} = 0?

Answer: The number of possible orbitals = 1.

### Define Orbitals in Quantum Physics or Chemistry

Atomic orbitals define the basic building blocks of the orbital diagram or alternatively known as the electron wave mechanics model. According to the electron wave model, an orbital defined as a region in space where the probability of finding an electron maximum. Therefore, the probability of finding the electron wave in the 1s-orbital of the hydrogen uses certain positions near the nucleus. And electron density maximum in the region just surrounded the nucleus of an atom.

But according to the electron wave model, the wave function of the electron in an atom is called orbital. Thus the probability of finding an electron in space around the nucleus involves two aspects, radial, and angular probability. It is not possible to represent an orbital completely in one diagram on paper. Hence angular probability distribution mutually combined to form the overall magnetic shapes of the orbitals.

### Shape of s-orbital in an Atom

The angular probability distribution greater interacts and important for s-orbital. But the s-electron has no angular dependence because the relevant wave function is independent of angles θ and Φ.

Thus the sphere of a definite radius represents the probability of finding the electron cloud in s-orbital. The electron cloud distribution in s-subshell has a spherically symmetrical probability distribution.

### Shape of p-orbitals of an Atom

The magnetic quantum number of p orbital 1, 0, -1. Hence p-orbitals define by three orientations in space and these orientations represented as p_{x}, p_{y}, and p_{z}. So these subshells mutually perpendicular and concentrated along the respective coordinate axis X, Y and Z. But unlike the s-orbital, the angular part of the p-wave dependent on θ and Φ and p-subshell shielding by s-electron of an atom.

### Shape of d-Orbitals

When n =3, the orbitals start with the 3rd main electron energy levels of an atom, l = 2(d – orbital), and m_{l} = -2, -1, 0, 2, 1. Therefore, d-orbital has five orientations in space represents

But the absence of a magnetic field all these five d orbitals are equivalent. Therefore, the electron energy levels of these five d-orbitals in quantum mechanics forming a set five-fold degenerate energy level and the shapes diagram dimensions of these orbitals identify by the principal, azimuthal, magnetic, spin quantum number or numbers of the atom for physics or chemistry courses.