Heisenberg Uncertainty Principle An electrons location and speed cannot be determined at the same time. If we cause change to find one variable, we are no longer looking at the actual e- situation. If we need to slow or stop it to locate it or if we need to locate it to find its speed, then we allow the chance of change. So quantum mechanics can tell us the probability that an electron is somewhere, but it does not tell us how it got there.
Nodal Surfaces A nodal surface is a region that defines the border of an orbital. This is where the probability function equals zero. Electrons CAN NOT exist in this area. Nodal surfaces are spherical for the s orbitals. 3s orbital Nodal surfaces are NOT spherical for other orbitals. 2p orbital
Max Planck Max Planck mathematically determined h that could be multiplied by to solve for energy (E) every time an electron gave off light as it fell. (This simply means that all wavelengths are proportional) E = h
Bohr Model Bohr was able to calculate the energy for the allowed orbits of the hydrogen atom using the formula: Since this is true of any level, Bohr postulated the energy between energy levels could be calculated as well:
Bohr Model Emission Spectra explains Hydrogen Electrons exist in quantized energy levels As electrons drop to lower energy levels emitting quanta of energy which translate to frequencies & wavelengths Energy (Joules) Principle Energ y Level (n) Ratio of Level 1:Level X -2.18E-1811 -5.45E-1924 -2.42222E-1939 -1.3625E-19416 -8.72E-20525 -6.05556E-20636 -4.44898E-20749
Energy of Electrons We can calculate the energy the electrons of a hydrogen atom emits when they fall by using the Balmer equation So if an electron falls from the 3 rd energy level to the 2 nd energy level then – Note: energy levels are not actually distances between electrons and the nucleus.
Bright-line Spectra Atoms are quantized, existing only in definite energy states when an atom absorbs a specific quanta of energy electrons jump to higher energy levels. An EXCITED electron jumps from its ground state to a higher energy level. The energy cannot be maintained so it falls back to where it came from losing exactly the same amount of energy that it absorbed.
De Broglie Small matter (electrons) have wavelike properties as well. Changed the Bohr model so that all elements could be explained according to their frequencies of energy. Remember that energy is constant and that standing waves are quantized as well (they only increase by multiples of ½)
De Broglie Essentially the model went from Bohr to de Broglie
de Broglie and Wave Model An electron in its path is associated with a wavelength. The wavelength depends on the mass:
Example Problem What is the characteristic wavelength of an electron with a velocity of 5.97 x 10 6 m/s? (Use 9.11 x 10 -31 kg for the mass of an e - )