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# Quantum Number

## What are quantum numbers?

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

To define the orbitals and fine structure of atoms four quantum number is needed to explain the various absorption or emission spectrum of photon particle. These numbers in quantum mechanics are the identification number for individual electron particles in an atom to describe the position and orbital 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. ### What is principal quantum number?

The principal quantum number describes the set of energy levels or the principal shell in 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 model of hydrogen atom, the energy set of the hydrogen energy levels is fixed in the fixed value of n.

#### How to find principal quantum number?

But the energy value of each electron depends mostly on the principal quantum number of an orbital in 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.

### What is azimuthal quantum number?

The azimuthal quantum number was introduced by Sommerfeld in his atomic structure. Therefore Sommerfeld gives the angular momentum of an electron in its elliptical movement around the nucleus of an atom. Therefore, the general geometric shapes of an electron cloud or orbitals define by the azimuthal or angular momentum quantum number.

#### How to find azimuthal quantum number?

Permitted values of l for a given value of n have 0 to (n-1). Therefore, the magnetic quantum numbers, l = 0, 1, 2, 3…..(n – 1). But the total number of different values of l equal to n.
When n = 1, l = 0 or 1s-orbital. But for n = 2, l = 0, 1 or 2s, 2p-orbitals. When n = 3, l = 0, l, 2 or 3s, 3p, and 3d-orbitals.

### What is 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 a magnetic field or the presence of the electric field. Therefore, 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 the magnetic quantum number for electronic orbitals.

#### Magnetic quantum number formula

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

### What is spin quantum number?

When spectral lines of hydrogen, lithium, sodium, and potassium are observed by the instrument of high resolving power. Each of the lines of the spectral series was found to consist of a pair of quantum lines known as a 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 is regarded as a small magnet. A beam of the hydrogen spectrum can split into two beams by a strong magnetic field.

#### Spin quantum number formula

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 in the sub-orbitals. The spin quantum number independent of the other three numbers. Because two directions of spin have two possible spin values (+ ½) and (- ½) for an orbital. Therefore, these values depending on the direction of rotation of the axis of the electron.

### How to find quantum numbers?

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, 1s2 2s2 2p6 3s2 3p6 4s1 3d5. The 19th electron means 4s1 electron. Therefore, the calculated quantum number for 19th electron, n = 4, l = 0, m = 0, s = +½.

Question: Identify the correct set of 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 the principal quantum number equal to four?

Answer: Numbers of possible orbitals when principle quantum number equal to four, [1 (4s) + 3 (4p) + 5 (4d) + 7 (4f)] = 16.

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

Answer: With these quantum numbers set the number of possible orbitals equal to one.

### Atomic orbital diagram

Atomic orbitals define the basic building blocks of the quantum orbital diagram or alternatively known as the electron wave mechanics model. According to the electron wave model, an orbital is 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. Hence the electron density maximum in the region just surrounded the nucleus of an atom.

#### Orbital meaning in chemistry

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

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

### Shape of p-orbitals of an Atom The magnetic quantum number of p orbital 1, 0, -1. Therefore, the p-orbitals define by three orientations by three quantum numbers. These orientations are represented as px, py, and pz-orbitals. So these sub-orbitals 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-orbitals electron shielding by the 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. Therefore, the azimuthal and magnetic quantum numbers equal to 2(3d-orbital), and -2, -1, 0, 2, 1 respectively. Hence d-orbital has five orientations in space represents as 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 mechanics forming a set five-fold degenerate energy level and the shape diagram dimensions of these orbitals identify by the principal, azimuthal, magnetic, spin quantum number or numbers of the atom for physics or chemistry courses.