Atom Models

• Dalton’s model
• J.J. Thomson’s model
• Rutherford’s model
• Bohr’s model
• de Broglie’s concept
• Heisenberg’s uncertainty principle
• Quantum mechanical model – Schrodinger Equation
• Quantum numbers
• Filling of orbitals
  • Aufbau principle
  • Pauli Exclusion principle
  • Hund’s rule of maximum multiplicity
  • Shapes of orbitals

DALTON’S ATOMIC MODEL

• Atoms are indivisible.
• a-tomio = non-divisible (Greek)
• Basic unit that makes up all matter is atom.
• Failure – atom is divisible, sub-atomic particles such as proton, electron, neutron were later found out.

J.J.THOMSON’S ATOMIC MODEL

• J.J. Thomson’s cathode ray experiment showed that atoms consist of negatively charged particles (electrons).
• Atom is a positively charged sphere in which the electrons are embedded like the seeds of watermelon.

RUTHERFORD’S ATOMIC MODEL

• Rutherford’s alpha ray scattering experiment showed that Thomson’s model was wrong.
• He bombarded a thin gold foil with a stream of fast moving alpha particles and obtained the following results.
  1. most of the alpha particles passed through the foil.
  2. some of them were slightly deflected.
  3. very few alpha particles were bounced back.
• Based on these observation he inferred the following proposals.
  1. Atom contains lot of empty space.
  2. Electrons are revolving around the nucleus in cricular orbits.
  3. Nucleus is the centre mass occuping the least space.

1. Source of alpha particles
2. Lead block shield
3. Photosensitive zinc sulphide screen
4. Gold foil
5. Some deflected alpha particles
6. Most undeviated alpha particles
7. A few bounced alpha particles

• Failures – A moving charged particle continuously loose its energy in the form of radiation. The moving electron will hit the central nucleus by loosing its energy gradually and developing a spiral path. This causes a self destruction of atom.

BOHR’S ATOMIC MODEL

• The energies of electrons are quantised.
• The electron is revolving around the nucleus in circular stationary orbits.
• The electrons possess angular momentum (mvr) and that is equal to integral multiples of h/2π.
• mvr = nh/2π
  • m = mass of electron
  • v = velocity of electron
  • n = integer
  • h = Planck’s constant
• When an electron revolves in a stationary orbit, it does not loose its energy.
• However, when the electron jumps from higher energy state (E2) to lower energy state (E1), the excess energy is emitted as radiation.

• When the electron in lower energy state (E1) absorbs an energy, it jumps to higher energy state (E2).

1. n = 3 (Third energy level) = M shell
2. n = 2 (Second energy level) = L shell
3. n = 1 (First energy level) = K shell
4. Increasing energy orbits
5. Nucleus
6. Electron orbits
7. Electron
8. Emission of radiation, (E3 – E2) = hν

• Radius of nth orbit (rn)is given by

• Energy of the electron revolving in the nth orbit is given by

• Energy of the electron in the nth orbit is also given by

• Limitations of Bohr’s concept
  1. Applicable to species having one electon system only (H, Li2+)
  2. Not applicable to multi electron atoms.
  3. Unable to explain Zeeman effect and Stark effect.
  4. Zeeman effect: the splitting of spectral lines in the presence of magnetic field.
  5. Stark effect: the splitting of spectral line in the presence of an electric field.
  6. Unable to explain revovling of electrons in fixed orbit.

de Broglie Concept

• All forms of small particles of matter show wave and particle nature. (Dual nature of matter).
• According ot Planck’s quantum hypothesis, the energy is given as photon (hv), where v = frequency, h = Planck’s constant.
• According to Einstein, E = mc^2
• de Broglie combined these two equations as follows.

For a particle having mass m and moving with a velocity, v, the wavelength is given by

This equation is permitted only when the particle travels at the speed much less than that of light. The light velocity, c is replaced with matter velocity, v. Momentum, p is given by mv.

• Higher the momentum, less will be the wavelength.
• Lower the mass, higher will be the wavelength.
• Therefore, electron like particles having mass in the order of 10^-31 kg have the wavelength larger than the size of atom. Wavelength is significant.

Quantisation of Angular momentum by de Broglie concept

• The electrons revolving around the nucleus exhibit particle and wave nature.
• Circumference of the orbit of electron is given by

HEISENBERG’S UNCERTAINTY PRINCIPLE

• It is not possible to determine both position and momentum of a microscopic particle simultaneously and accurately.

Δx = uncertainty in measuring the position

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Δp = uncertainty in determining momentum

• For macroscopic objects the uncertainty is insignficant.

QUANTUM MECHANICAL MODEL (Schrodinger Equation)

• The dual nature of microscopic particles cannot be explained by classical mechanics.
• Schrodinger explained the dual nature by quantum mechanics using differential equation.
• The time independent Schrodinger equation is given by

• The above equation is called time independent Schrodinger wave equation.
• The total energy, E is quantised, indicating the permitted total energy values only.
• These permitted energy values are called eigen values.
• The corresponding wave functions represent the atomic orbitals.

What are the features of the quantum mechanical model of atom?

1. The energy of electrons in an atom is quantised.
2. The solutions of Schrodinger wave equation gives the allowed energy levels. They are called orbitals or sub-energy levels.
3. Orbital is a three dimensional space within which the probability of finding out the electron is maximum.
4. The wave nature of electron in an orbital can be defined by the wave function.
5. The probability density is always positive as given below.

QUANTUM NUMBERS