At the initial point of the 19th century, a British chemist John Dalton proposed the atomic theory. This could successfully explain the law of conservation of mass and constant proportion. However since he considered atoms to be indivisible, his theories couldn’t be used to explain many chemical phenomena.

By the end of the 19th and beginning of the 20th century, several experimental results helped the existence of subatomic particles.

Faraday experimented on partially evacuated tubes called cathode-ray tubes. He found the existence of cathode ray particles or electrons which are a basic constituent of all atoms. J.J. Thomson found out the charge to mass ratio of electron and Millikan found out the charge on each electron.

Canal rays were discovered when electric discharge was carried out in modified cathode tubes. These rays were positive gaseous ions. The smallest ion was found from hydrogen which was called a proton.

Chadwick discovered electrically neutral neutrons when he bombed a thin sheet of beryllium using alpha particles.

**Atomic models**

After the discovery of protons, neutrons and electrons it was a challenge to predict the internal structure of the atom to account for the stability and behavior of the atom and also the reason why atoms combined to form compounds.

J.J. Thomson presented the **plum pudding model** where he considered the atom to be a uniform positive sphere with the electrons embedded in it such that it has the most stable electrostatic arrangement. This model was discarded as it couldn’t explain the results of later experiments.

Ernst Rutherford performed the **gold foil α-particle scattering experiment** and got very interesting results. A stream of high energy α-particles was directed at a very thin gold foil. A zinc sulfide screen was set up such that when the particles got deflected they would hit the screen and cause a tiny flash of light. Most of the α-particles could pass through the foil UN-deflected indicating that most of the space in the atom is empty. A few particles were deflected by small angles and very few were deflected by 180 degrees. This means there is a high repulsive force by positive charges which are densely concentrated in a very small area which is the nucleus. The electrons move in circular orbits around the nucleus and the nucleus and electrons are held together by electrostatic forces.

But the Rutherford model has some flaws. Any particle moving in a circle has some acceleration as direction keeps changing. According to Maxwell theory charged particles (electron) releases electromagnetic radiation on acceleration. Thus the energy of electron should slowly reduce and it should have fallen into the nucleus. But atoms are stable.

Neils Bohr proposed his **quantized shell model** of the atom to explain how electrons can have stable orbits. In this model, electrons move in orbits of fixed size and energy(allowed energy states or stationary states) and do not radiate energy. They only radiate or absorb energy when they move from one orbit to another. Smaller orbit has lower energy. This model failed to explain why atoms form chemical bonds and combine, and spectral lines (doublets) of atoms in spectroscopy experiments.

__Quantum mechanical model of an atom__

This model was founded on two basic principles – dual behavior of matter and Heisenberg uncertainty principle. Dual behavior states that matter has both wavelike and particle-like properties. Heisenberg uncertainty principle states that it’s impossible to determine both momentum(speed) and position of an electron simultaneously. Thus this rules out the existence of definite orbits of electrons and the path cannot be known accurately.

When we solve **Schrodinger equation **(developed for quantum mechanics) the solutions are the possible energy levels(quantized energy states) the electron can occupy. It also gives the wave function which gives all the information and path of the electron in that energy state. These wave functions give us three quantum numbers – principal quantum number(n), azimuthal quantum number(l) and magnetic quantum number(m).

The wave function is a mathematical function. Its value depends on the coordinates of the electron. It doesn’t have any physical significance. The probability for finding an electron at a certain point is a square of the wave function value at that point.

The Schrodinger equation can be used easily for a single-electron system like hydrogen (depends on n) but in multi-electron systems, due to increased nuclear charge there is an orbital contraction, so approximations need to be applied(depends on n and l).

__ORBITALS__

Orbitals are characterized by their size(given by n), shape(given by l) and orientation(given by m).

A smaller size means more probability of finding the electron near the nucleus. Orientation gives the direction along which the probability of finding electrons is higher.

**The principal quantum number **gives the size and energy of the orbital. It gives the principal shell number of the electrons. If the shell number is n then the number of orbitals is square of n is higher then, further will be the electron from the nucleus.

n = 1 2 3 4…

Shell= K L M N…

**Azimuthal /orbital angular momentum quantum number **defines the three-dimensional shape of the orbital. For a particular value of n the values of l range from 0 to n-1

For n=4 we have l=0,1,2,3

Each principal she’ll has a number of subshells whose value is equal to the n of that shell. Thus for n=2, there are two subshells. Each subshell has a definite azimuthal quantum number.

Value of l = 0 1 2 3

Notation = s p d f

**A magnetic orbital quantum number **gives the orientation of the orbitals with respect to a predefined coordinate axis. For a definite subshell l, (2l +1) values of m are possible ranging from -l to +l

For l=2 m= -2,-1,0,1,2 thus 5 orbitals present.

**The spin quantum number** gives the direction of spin of an electron around its own axis (+½ and -½ ). Thus two spin states are possible and an orbital can have only 2 electrons of opposite spin states.

__Orbital shapes__

The s orbital is spherical in shape. Probability of finding electrons is the same at a given distance in all directions, spherically symmetric.

The p orbitals are dumbbell-shaped. There are 3 orbitals possible, each oriented along one coordinate axis with a node in the center.

The d orbitals are double dumbbell-shaped with nodes at the center. Five orbitals are possible(dxy, dyz, dzx, dx2-y2, dz2) with the following orientation.

A **node **or **nodal surface **indicates a place where the probability of finding an electron is zero. Two types of nodes are possible – radial nodes and angular nodes. The total number of nodes is n-1 which is the sum of radial nodes (l) and angular nodes(n-l-1).

__Energy of orbitals__

As per the *Aufbau* principle, in an atom at ground state, the electrons are filled first in the orbitals from lowest energy and then in the orbitals of highest.

If the value of (n+l) is lower, lower is the energy. If two or more orbitals have the same (n+l) value, then the orbital with lower ‘n’ has lower energy. The order of filling electrons is like :

1s, 2_{S}, 2_{P}, 3_{S}, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 4f, 5d, 6p, 7s and so on.

There are few exceptions to this rule when the orbitals are of the almost same energy or when we can achieve extra stability due to half-filled or fully filled orbitals like chromium ([Ar] 3d5 4s1) and copper ( [Ar] 3d10 4s1). Here the orbitals are half-filled and fully filled respectively giving the atoms higher stability.

**By Pauli exclusion principle, **no two electrons can have the same set of 4 quantum numbers. As each orbital has 2 electrons of opposite spins so inappropriate shell n, the number of orbitals is square of n and the number of electrons is twice the square of n.

**Hund’s rule of maximum multiplicity **states that pairing of electrons in an orbital does not occur until each orbital of that subshell has one electron each.

The distribution of electrons in atoms is called the **electronic configuration** of the atom.

The electronic configuration of the first 10 elements are as follows :

Hydrogen 1s1

Helium 1s2

Lithium 1s2 2s1

Beryllium 1s2 2s2

Boron. 1s2 2s2 2p1

Carbon 1s2 2s2 2p2 (see carbon configuration)

Nitrogen 1s2 2s2 2p3

Oxygen 1s2 2s2 2p4

Fluorine 1s2 2s2 2p5

Neon. 1s2 2s2 2p6