Quantum Mechanical Model of the Atom Chapter 6 Part III

Bohr’s model was Imperfect The model of an electron in a circular orbit around a nucleus worked only for Hydrogen, Lithium but by Boron, the model was ineffective.

Electrons bound to the nucleus seemed similar to a standing wave. See if video works

De Broglie, Heisenberg and Schrödinger pioneered wave mechanics, aka Quantum Mechanics. ArtsSciences/physics/PhysicsInitiative/Physics2 000/quantumzone/debroglie.html ArtsSciences/physics/PhysicsInitiative/Physics2 000/quantumzone/debroglie.html This site shows how a particle such as an electron can have wave-like functions. ure3/l3u4.htm ure3/l3u4.htm This site demonstrates wave like qualities of orbitals.

Schrödinger & de Broglie Both felt the electron acted like a standing wave. (see slinky) Theorizing that the electron acts like a wave, and has a wave function  That represents the x, y and z coordinates of the electron. A specific wave function is often called an orbital.

By treating the electron as a wave: Schrödinger mathematically described a series of wave functions each having discrete energy levels.

Heisenberg’s Uncertainty Principle ∆x * ∆ (mv) > h/4  x= the uncertainty of the particle’s position mv = the uncertainty of the particle’s momentum h = Planck’s constant Stating that we cannot know both the speed and position of an electron

Heisenberg’s big idea ture3/l3u4.htm ture3/l3u4.htm This url demonstrates how the model of a circular orbit (Bohr) morphs into a model demonstrating the Uncertainty Principle. Electron clouds as orbitals.

Wave Functions [  (X 1, Y 1, Z 1 )] 2 = N 1 [  (X 2, Y 2, Z 2 )] 2 N 2 N 1 /N 2 gives the ratio of the probability of finding the electron at position 1 relative to position 2. If the number is 100, the electron is 100 times more likely to be in position 1 than 2.

Probability Distribution This square of the wave function is represented as a probability distribution. AKA electron density map.

When the electron density map is divided into equal spheres, the plot of finding the electron in each successive sphere gives the following curve

The size of an atom The definition of the size of a hydrogen atom 1s orbital is the radius of the sphere that encloses 90% of the total electron probability.

Quantum numbers When solving Schrödinger's equation for the hydrogen model we find wave functions / orbitals. Each orbital is characterized by a series of numbers called Quantum Numbers.

Principle Quantum number n has intergral values 1, 2, 3… n is related to the size an energy level of the orbital. Or n= energy level

Angular quantum number l has integral values of 0 to n-1 for each value of n. Each value of l has a shape associated with it. 0= s 1=p 2=d 3=f

Magnetic quantum number m is related to the orientation of the orbital and may equal any integral value between l and – l. This includes zero. It relates to the orientation of the orbital in space relative to other orbitals in the atom.

Spin Each orbital may hold two electrons. Quantum number are +1/2 and -1/2

Nodes See handout