Rutherford Atomic Model

•Nucleus as Positive Centre.

•Electrons revolving round the nucleus in oblong orbital.

•Electrons moving very fast around the nucleus in oblong orbital.

•Lots of empty spaces inside an atom around the nucleus and the orbital.

(WITH THE HELP OF Alpha SCATTERING EXPERIMENT of Au, Ag, Pt, Cu)

Bohr’s Atomic ModelDRAWBACKS of Rutherford:• Rutherford not able to Xplain Y the ‘e’ s moving around the nucleus with

acceleration and emitting electromagnetic radiations, under the influence of Centripetal Force, collide with the Nucleus in less than 10-8 seconds.

• Also Y do the electronic orbitals have different energies (Energy Levels)

These drawbacks were xplained by Bohr’s Model along with helps from Maxwell

Electromagnetic Radiation Theory & Louis De Broglie’s Equation for Duality of

Matter.

De Broglie’s Equation for Duality of Matter

• Maxwell and De Broglie proved that an electron behaves both as a particle as well as a wave emitting radiation of electromagnetic nature.

• De Broglie thought that, if the double aspect, i.e., the duality of the wave nature and the particle nature, it is valid not only for light but also for such substance particles like electrons.

• Max Planck stated that when radiant energy is either emitted or absorbed by a body they happen in the form of small packets of energy, called QUANTUM.

• The energy of 1 QUANTUM α frequency of radiation,

E α ν

E = h ν

[where h is Planck’s Constant (h = 6.6 x 10-34 J sec)]• Einstein in 1905 further simplified Max Planck’s

Quantum Theory with respect to De Broglie’s relations which connect the particle and wave aspects in light quanta.

Maxwell Electromagnetic Theory• Maxwell stated that any body moving about in oblong circular path (as

stated by Rutherford) will emit radiation and under the influence of Centripetal Force will collide with the Nucleus under 10-8 seconds.

• According to Maxwell, the frequency (ν) of classical radiation by an ‘e’ is equal to the rotational frequency (νrot) of the ‘e’ in the orbit.

ν α νrot

• It should also have an Angular Momentum (L).

L = mevr,

(where me = mass of an ‘e’

v = velocity of an ‘e’

r = radius of it’s orbit)

Line Spectrum of Hydrogen (Bohr & Rydberg)• When an electric current is passed through a glass tube that contains hydrogen gas at

low pressure the tube gives off blue light.• When this light is passed through a prism, four narrow bands of bright light are

observed against a black background.

• These narrow bands or lines have the characteristic wavelengths and colors shown in the table below.

Wavelength Color

656.2 red

486.1 blue-green

434.0 blue-violet

410.1 violet

• Each of these lines fits the same general equation, where n1 and n2 are integers and RH is 1.09678 x 10-2 nm-1 or 109,677 cm-1

Bohr’s Theory n’ ModelMODEL OF ATOM: Depending on all the theories of Maxwell and De Broglie, Bohr

stated his atomic model as:• ‘e’ s revolve around nucleus in definite circular paths called orbitals.• Each orbit is associated with definite E and therefore Shells also known as Energy Levels. • Orbital or Energy Levels can be represented starting from the capital letter, K as 1, L as 2,

M as 3, N as 4……• As long as an e stays in a particular orbital, it stays neutral, i.e., it won’t emit or absorb E.

• If E is supplied to the atom, e absorbs E only in certain fixed amounts called Quanta and

jumps to the higher E state. The Excited state (E2), however, is unstable. Hence it emits the

same amount of E as it had absorbed and comes back to the Ground state (E1). The

difference in E can be calculated as

ΔE = E2 – E1 • ONLY those Energy Levels are permitted for an ‘e’ where Angular Momentum of ‘e’ (mvr)

= a whole number multiple of h/2π, i.e.,

mvr = n x h/2πACHIEVEMENTS OF BOHR MODEL:• He was able to explain the Stability of an Atom.

• Bohr’s Theory also explained the Atomic Spectrum of H2

DRAWBACKS OF BOHR’S MODEL

• While creating his model, he did not consider the wave character of an ‘e’.• According to Bohr Model, an ‘e’ revolves around a definite path and the path can be

known only if ‘e’ s velocity and position is known. That according to Heisenberg is impossible.

HEISENBERG’S UNCERTAINTY RULEThe lead up to the failure of Bohr’s model paved the way for certain other principles,

specially, those of Heisenberg’s Uncertainty Rule, Afbau’s Principle, Pauli’s Exclusion

Principle and Hund’s Multiplicity Rule amounting to a completely new model that we

now know as Quantum Mechanical Model of an Atom.

Heisenberg’s Uncertainty Rule states that its is IMPOSSIBLE to determine the velocity

and the position of an ‘e’ simultaneously.

ΔX x ΔPx >= h/4π

ΔX x Δmvx >= h/4π

ΔX x Δvx >= h/4πm

QUANTUM MECHANICAL MODEL OF AN ATOM

This paved the way for the Modern Atomic Theory with the help of some imp.

principles like, Aufbau’s Principle, Hund’s Multiplicity Rule, Pauli’s Exclusion

Principle.• The E of ‘e’ s in an atom is said to be Quantized, i.e., having singular specific

values.• The existence of quantized ‘e’ is a direct result of the Wave character of the

‘e’ s.• It’s almost impossible to determine the velocity and exact position of an ‘e’ in

an Energy level simultaneously.• An atomic orbital or energy level always has a Wave func:, called ψ (si).• There can be many orbitals or energy levels in an atom depending on Atomic

Number. An orbital cannot have more than 2 ‘e’ (this law was modified at a later stage).

Atomic Orbitals can be specified by quoting their corresponding energies, which

can be expressed in terms of QUANTUM NUMBERS.

QUANTUM NUMBERS4 types of Quantum Numbers exist. They are used for getting complete set of

information

on an ‘e’ in an atomic orbital – location, energy, spin etc. They are :• Principal Quantum Number (n) – helps to determine energy level • Azimuthal Quantum Number (l) – helps to determine shape of orbital• Magnetic Quantum Number (m) – helps to determine orientation of the ‘e’

(NOTE: the values of n, l, m are all interdependent on each other)• Spin Quantum Number (s) – independent of the first three quantum numbers

because s is always = –½ or +½

Each electron in an atom has a unique set of quantum numbers. No two electrons

can share the same combination of four quantum numbers. Quantum numbers are

very significant because they can determine the electron configuration of an atom.

Principal Quantum Number (n) – helps to determine energy level

or shell where the ‘e’ belongs to.

Denoted by the letter, n. Values can be any integral number, except

0.

For K shell, n = 1

For L shell, n = 2

For M shell, n = 3

For N shell, n = 4 (K is the first shell starting from the Nucleus)

Azimuthal Quantum Number (l) – helps to determine

• shape of orbital• the number and shape of sub – shells present in each principal shell• the relative energies of various sub – shells

Denoted by the letter, l. Values of l dependent on n and can have values ranging

from 0 to n – 1.

For K shell, n = 1, l = 1 – 1 = 0

For L shell, n = 2, l = 2 – 1 = 1

For M shell, n = 3, l = 3 – 1 = 2 and so on…..

Spin Quantum Number (s) - independent of the first three quantum

numbers because s is always = –½ or +½ • The Spin Quantum Number (s) has a value that is ½ the value of angular

momentum of an electron (mvr). • An electron spins around an axis and has both angular momentum and orbital

angular momentum. • As angular momentum is a vector, the Spin Quantum Number (s) has both a

magnitude (1/2) and direction (+ or -).

Magnetic Quantum Number (m) – helps to determine orientation

of the ‘e’ within a sub shell and the number of orbitals.

Its value depends on the Azimuthal Quantum Number (l).

Given a certain value of l, m has a value ranging from –l to +l

including 0.

Rules for filling up of Atomic Orbital / Shell

Aufbau’s Principle/Pauli Exclusion Rule/Hund’s Rule: • It is used to determine the electron configuration of an atom• It is a hypothetical process in which an atom is ‘built up’ by

progressively adding electrons.• As electrons are added, they assume their most stable conditions.• Electrons fill orbitals starting at the lowest available energy

levels before filling higher levels (e.g. 1s before 2s).• According to Pauli’s Rule, the number of electrons that can occupy

each box is limited, i.e., 2.• Hund's rule states that unoccupied orbitals will be filled before

occupied orbitals are reused (by electrons having different spins).

Formulae for Numericals

Mass of e- = 9.1 x 10-28 g/ 9.1 x 10-31 Kg

Charge of an e- = -1.6 x 10-19 C

e/m Ratio = 1.7 x 1011 C/Kg

Mass of p+ = 1.6 x 10-24 g/ 1.6 x 10-27 Kg

Charge of p+ = +1.6 x 10-19 C

Avogadro’s No. = 6.022 x 1023

Z = No. of e- = No. of p+

A = No. of p+ + No. of n

IMPORTANT RELATIONS TO REMEMBER

Relation of Frequency and Wavelength

ν = c/λ

Wave Number

ν = 1/λ

Energy of a Photon/ Electron

E = hν

Again, ν = c/λ

E = hc/λ

De Broglie’s Equation

λ = h/mv

Kinetic Energy

KE = 1/2mv2

Bohr’s Theory

mvr = nh/2π

ENERGY LEVELS of ORBITALSEnergy — GROUND state and EXCITED states:• The energy (E) associated with that of an ‘e’ is attributed to its orbit.• The E of an Electronic Configuration of an atom is said the be the sum of the energies

of all the electrons.• The configuration that corresponds to the lowest electronic energy is called the

GROUND state.• Any other configuration is an EXCITED state.

REFERENCES

• http://chemwiki.ucdavis.edu• http://chemwiki.ucdavis.edu/Physical_Chemistry/Qua

ntum_Mechanics/Atomic_Theory/Electrons_in_Atoms/Electron_Spin

• Wikipedia• MSU (Michigan State University) Online• Chemistry Full Marks• Nootan’s Chemistry XI• My own notes

Thank You!

Mr. Arunava Das#

(# Dept. of Cell and Molecular Biology, Indian Institute of Science, Bangalore),

Dept. of Chemistry,

GD Goenka Public School, Siliguri