Bohr and Quantum Mechanical Model Mrs. Kay Chem 11A

Those who are not shocked when they first come across quantum theory cannot possibly have understood it. (Niels Bohr on Quantum Physics)

Wavelengths and energy Understand that different wavelengths of electromagnetic radiation have different energies. c=vλ c=velocity of wave v=(nu) frequency of wave λ=(lambda) wavelength

Bohr also postulated that an atom would not emit radiation while it was in one of its stable states but rather only when it made a transition between states. The frequency of the radiation emitted would be equal to the difference in energy between those states divided by Planck's constant.

E 2 -E 1 = hv h=6.626 x Js = Plank’s constant E= energy of the emitted light (photon) v = frequency of the photon of light This results in a unique emission spectra for each element, like a fingerprint. electron could "jump" from one allowed energy state to another by absorbing/emitting photons of radiant energy of certain specific frequencies. Energy must then be absorbed in order to "jump" to another energy state, and similarly, energy must be emitted to "jump" to a lower state. The frequency, v, of this radiant energy corresponds exactly to the energy difference between the two states.

In the Bohr model, the electron is in a defined orbit Schrödinger model uses probability distributions for a given energy level of the electron.

Orbitals and quantum numbers Solving Schrödinger's equation leads to wave functions called orbitals They have a characteristic energy and shape (distribution).

The lowest energy orbital of the hydrogen atom has an energy of x 10 ­18 J and the shape in the above figure. Note that in the Bohr model we had the same energy for the electron in the ground state, but that it was described as being in a defined orbit.

The Bohr model used a single quantum number (n) to describe an orbit, the Schrödinger model uses three quantum numbers: n, l and m l to describe an orbital

The principle quantum number 'n' Has integral values of 1, 2, 3, etc. As n increases the electron density is further away from the nucleus As n increases the electron has a higher energy and is less tightly bound to the nucleus

The azimuthal or orbital (second) quantum number 'l' Has integral values from 0 to (n-1) for each value of n Instead of being listed as a numerical value, typically 'l' is referred to by a letter ('s'=0, 'p'=1, 'd'=2, 'f'=3) Defines the shape of the orbital

The magnetic (third) quantum number 'm l ' Has integral values between 'l' and -'l', including 0 Describes the orientation of the orbital in space

nlSubshellmlml Number of orbitals in subshell 303s01 13p-1,0,+13 23d-2,1,0,+1,+25 For example, the electron orbitals with a principle quantum number of 3

the third electron shell (i.e. 'n'=3) consists of the 3s, 3p and 3d subshells (each with a different shape) The 3s subshell contains 1 orbital, the 3p subshell contains 3 orbitals and the 3d subshell contains 5 orbitals. (within each subshell, the different orbitals have different orientations in space) Thus, the third electron shell is comprised of nine distinctly different orbitals, although each orbital has the same energy (that associated with the third electron shell) Note: remember, this is for hydrogen only.

SubshellNumber of orbitals s1 p3 d5 f7

Practice: What are the possible values of l and m l for an electron with the principle quantum number n=4? If l=0, m l =0 If l=1, m l = -1, 0, +1 If l=2, m l = -2,-1,0,+1, +2 If l=3, m l = -3, -2, -1, 0, +1, +2, +3

Problem #2 Can an electron have the quantum numbers n=2, l=2 and m l =2? No, because l cannot be greater than n-1, so l may only be 0 or 1. m l cannot be 2 either because it can never be greater than l

In order to explain the line spectrum of hydrogen, Bohr made one more addition to his model. He assumed that the electron could "jump" from one allowed energy state to another by absorbing/emitting photons of radiant energy of certain specific frequencies. Energy must then be absorbed in order to "jump" to another energy state, and similarly, energy must be emitted to "jump" to a lower state. The frequency, v, of this radiant energy corresponds exactly to the energy difference between the two states. Therefore, if an electron "jumps" from an initial state with energy Ei to a final state of energy Ef, then the following equality will hold: (delta) E = Ef - E i = hv To sum it up, what Bohr's model of the hydrogen atom states is that only the specific frequencies of light that satisfy the above equation can be absorbed or emitted by the atom.