# Atomic Models and Quantum numbers

### Atomic Models:

To show the arrangement of fundamental particles in an atom various models were proposed, some important models are as follows:

Dalton’s Atomic Theory:

The different assumptions of this theory are as follows;

- All matters are made up of atoms which are indivisible and indestructible.
- All the atoms of a given element have identical properties including identical mass.
- Atoms combine in small whole numbers to form compound
- Chemical reactions involve only combination, separation or rearrangement of atoms.

Thomson’s Atomic Model:

- Every atom consist of uniformly positively charge sphere having radius in the order of 10-10 m in which entire mass is uniformly distributed and negatively charges electrons are embedded randomly.
- Thomson uses the cathode ray tube to gives its atomic model.
- This model is known as plum pudding model.
- According to him negative charge particles are distributed in atom and to balance this negative charge some positive charge particles also present in it.
- The atom as a whole is neutral.

Drawbacks of Thomson’s Atomic Model:

- It could not explain the origin of spectral series of hydrogen and other atoms.
- It could not explain large angle scattering of alpha particles.

Rutherford’s Atomic Model:

- He fired a beam of alpha particle on a sheet of gold to gives its model theory.
- The existence of nucleus was proved by Rutherford in his alpha particle scattering experiment.
- The entire positive charge and almost entire mass of atom is concentrated at its centre in a very tiny region of the order of 10-15m, called nucleus.
- The negatively charged electrons revolve around the nucleus in different orbits.
- Total positive charge on nucleus is equal to the total negative charge on electron; therefore atom as overall is neutral.
- A nucleus consists of positively charged protons and electrically neutral neutrons.

Limitations of Rutherford’s Atomic models:

- According to Maxwell electromagnetic wave theory an accelerated charged particles emits its energy in the form of electromagnetic waves. Therefore an electron must emit emits energy during its course of accelerated motion around the nucleus. Due to which the radius of its path will decrease gradually and ultimately it will fall in the nucleus.

Plank’s Quantum Theory:

Planck gave a new revolutionary theory of radiation known as quantum theory of radiation.

According to this theory

Radiant energy is not emitted or absorbed continuously but discontinuously in the form of small packets of energy known as photons (quanta).

The amount of energy associated with a quantum of radiation is proportional to the frequency of radiation.

Energy = hÎ½

Where h is Planck’s constant

Bohr’s Model:

- Bohr’s model is based on the quantum physics i.e. quantization of energy
- This model is similar to planetary model in which electron revolves around the nucleus in specific orbit
- Bohr’s model is considered as the primitive hydrogen atom model
- Every orbit has a specific size and energy level.
- Smallest energy is found in the smallest orbit as energy is related to the size of the orbit.
- Electrons can move from one orbit to another by emitting or absorbing energies according to quantum mechanisms.

Heisenberg’s Uncertainty Principle:

- According to this theory the position and velocity or momentum cannot be measured at a single instant.
- Heisenberg principle is not applicable to macroscopic objects

De-Broglie Concept:

- De Broglie states that electron have dual nature i.e. wave nature and particle nature
- Wavelength (l) of an electron is inversely proportional to its momentum (p)

l=h/p=h/mv, here h is Planck’s constant

Shell:

The electron has a definite energy characteristic of the orbit in which it is moving. These orbit or energy levels or shells therefore also known as stationary orbits.

n=1,2,3,4

Shell =K,L,M,N

The shell with n=1 is closest to the nucleus and an electron in this level has the lowest energy as it is closest to the positive charge of the nucleus.

Distribution of electrons in different orbits:

- It was suggested by Bohr and Burry and rules that govern it are as follows:
- The maximum number of electrons present in a shell is given by the formula 2n2 where n=1,2,3 and 4 for K,L,M and N shells respectively.
- The maximum number of electrons that can be accommodated in the outermost orbit is 8.
- The shells are filled in a step-wise manner.

Electronic Configuration:

- It is the arrangement of electrons in various shells, sub-shells and orbitals in an atom.
- It is written as 2,8,8,18,32
- The maximum number of electron in a shell is given by 2n2

Filling or orbitals in Atoms:

The filling of electrons into orbitals of different atoms takes place according to the Aufbau Principle, Pauli Exclusion Principle and Hund’s rule of maximum multiplicity.

According to Aufbau principle in the ground state of an atom, electron enters the orbital of lowest energy first and subsequent electrons enter in the order of increasing energies.

Lower the value of (n+l) for an orbital, lower is its energy.

here l is the azimuthal quantum number and n indicates the principle quantum number

If two orbitals which have same (n+l) value, the orbital with lower value of n has lower energy.

Hund’s rule of maximum multiplicity deals with the filling of electrons into the orbitals belonging to the same sub-shell. According to this rule, electron pairing will not take place in orbital of same energy until each orbital is first singly filled with parallel spin.

Quantum Numbers:

Each electron in an atom is characterised by a set of definite values of three quantum numbers n, l and m. In addition of these three numbers, fourth quantum numbers is also needed which specifies the spin of the electron.

Principal quantum number (n):

Determines the main energy level of shell in which the electron is present.

The various values of n are 1, 2, 3 and 4 etc. also known as K, L, M and N etc. respectively, as the value of n increases energy of electron also increases.

Azimuthal quantum number (l) determines the sub-level or sub-shell(s, p, d and f) in a given principal energy level or shell to which an electron belongs.

Magnetic quantum number (m) gives the information about the orientation of the orbitals.

Spin quantum number(s) describe the spin orientation of the electron; the electron can spin only in two ways, i.e. clockwise or anticlockwise.

Pauli Exclusion Principle:

It states that no two electrons in an atom can have the same set of four quantum numbers.

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