Bohr’s Model Nucleus Electron Orbit Energy Levels Nucleus Electron Orbit Energy Levels
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