Bohr’s Model

Nucleus

Electron

Orbit

Energy Levels

Nucleus

Electron

Orbit

Energy Levels

The Bohr Model

• In 1913 Bohr provided an explanation of atomic spectra

• His model includes both classical and non-classical ideas

• His model included an attempt to explain why the atom was stable

• Bohr said classical view is wrong.

• Need a new theory — now called QUANTUM or WAVE MECHANICS.

Bohr Model

Bohr’s Assumptions

• The electron moves in circular orbits around the proton under the influence of the Coulomb force of attraction– The Coulomb force

produces the centripetal acceleration

Bohr’s Quantum Conditions

• I. There are discrete stable “tracks” for the electrons. Along these tracks, the electrons move without energy loss (Stationery State).

• II. The electrons are able to “jump” between the tracks.

In the Bohr model, a photon is emitted when the electron drops from a higher orbit (Ei) to a lower

energy orbit (Ef).

Ei-Ef=hf

Bohr Model: Orbit Radius

• Bohr assumed that the angular momentum of the electron was quantized and could have only discrete values that were integral multiples of h/2, where h is Plank’s constant

• mevr=nh/(2); n=1, 2, 3,…

• v=nh/(2 mer)

Bohr Model: Energy of electron in orbit

In each orbit, the energy of the electron is restricted to a certain value -

E = - RH/n2

RH is a constant in energy units:

= 2.179 X 10-18 J/atom

= 13.6eV/atom

= 1312 KJ/mole

Number of orbit = n = 1, 2, 3, etc.

When an electron changes orbits it changes energies.

•Energy is emitted in the form of light (electromagnetic radiation as the electron moves from a higher orbit to a lower one (from a higher energy level to a lower one).

•Energy is absorbed as electricity or heat as the electron moves from a lower to a higher orbit (energy level).

Specific Energy Levels

• The lowest energy state is called the ground state– This corresponds to n = 1– Energy is –13.6 eV

• The next energy level has an energy of –3.40 eV– The energies can be compiled in an energy level

diagram

• The ionization energy is the energy needed to completely remove the electron from the atom– The ionization energy for hydrogen is 13.6 eV

Energy Level Diagram

• The value of RH from Bohr’s analysis is in excellent agreement with the experimental value

• A more generalized equation can be used to find the wavelengths of any spectral lines

Orbit Radii and Energies

• rn=0.0529n2 (nm)

• En=-13.6/n2 (eV)

• Energy difference between the levels E=13.6(1/nf

2-1/ni2)

For example, between n=1 and n=2 (as drawn in the picture) E=13.6(1/nf

2-1/ni2)=13.6(1/12-1/22)=10.2 eV 

 

 

E=10.2 eV

Final state, nf

Initial State, ni

PROBLEMS WITH THE BOHR ATOM

A) It is only successful with the Hydrogen atomB) It could not account for extra lines in the H emission spectrum when a magnetic field was applied to the gas:

Zeeman Effect : Splitting of Spectral lines under the external magnetic fields

Stark Effect : Splitting of Spectral lines under the external electric field

C) PARTICLE-WAVE DUALISM

1923-24 - The French physicist de Broglie says that if light waves exhibit particle properties, under certain circumstances, then particles of matter should show wave characteristics under certain circumstances.

h = 6.63 X 10-34 kg m2/sec

if m is large and the speed is small, then is so small as to be meaningless- 10-34 m.

D) The idea of circular orbits and knowing where the electron is located is impossible:

In 1927 Werner Heisenberg showed from quantum mechanics that it is impossible to know simultaneously, with absolute precision, both the position and the momentum of a particle such as an electron. The Heisenberg Uncertainty Principle!

▲x * m▲v ≥ h/4