Chemistry AP Study Notes 6 (Orbitals)

The Electron Orbitals

• So the space around the nucleus of atoms has a certain structure. The clouds of probable location take on certain shapes. It's like a seating arrangement for the electrons. As people come in, they are given the next seat.
• There are shells of electrons, like rows of seats. These correspond to the periods or rows on the periodic table. We give them numbers, 1, 2, 3, 4...
• Within any shell, the first two electrons to arrive fill up a spherical orbital or subshell around the nucleus, which can hold two seats. So hydrogen's electron fills the first seat and the second seat is empty. Helium's two electrons entirely fill the first shell, which uniquely only holds two. It is a noble gas because it's outermost shell is completely full.
• A spherical orbital is called an s orbital (the similarity is coincidental). The first two columns of the periodic table are atoms whose outermost orbital involves one or two electrons in this spherical "seating." Group 1 has one electron in that shell. Group two has the spherical part of the shell full.
• After the first two electron seats, the next group of electron seats are also grouped in twos--two up and down, two in and out, and two side to side. So six possible seats perpendicular to each other. This orbital is called the p orbital (again, coincidental). The six groups on the right side of the periodic table are atoms whose outermost shell or valence shell involves electrons in the "p seats."
• When we get to the third row, the third shell, another type of orbital comes into play. However, it doesn't actually show up until the space of the fourth row. These are the transition metals. Ten electrons can fit in this orbital. There are 5 sets of two in interesting flower shapes.
• Finally, there is an f orbital with up to 14 electrons. These correspond to the Lanthanide and Actinoid elements usually placed at the very bottom of the periodic table.

Quantum Theory

• In the year 1900, a scientist by the name of Max Planck suggested that energy might only come in certain packets. So there is the base energy level, then twice that level, three times, etc. This is why there are fixed "seats" around the nucleus of an atom. There is no in between the seats. We say that the energy of an electron is quantized.
•  The starting point for an electron is its ground state. An excited state is when a certain amount of energy is added to the electron so it jumps to the next highest state. The energy between two levels is

ΔE = -2.18 x 10^-18 (1/n²_final – 1/n²_initial)

• In the 1920s, a man named Schrodinger came up with a wave equation to predict the possible size, shapes, and orientations that electron clouds could have around the nucleus. This is where the s, p, d, and f orbitals mentioned above come from. These states correlate to varieties of four quantum numbers.
• First there is the principal quantum number, which has to do with the shells, the rows or periods of the periodic table. n = 1, 2, 3...
• Then there is the angular momentum quantum number, which has to do with the orbitals. One less than n tells you how many orbitals exist for that row. So for the third shell, there can be L = 0, 1, and 2 (s, p, and d orbitals).
• The magnetic quantum number goes from -L to +L. So the p orbital (L = 1) has three options (-1, 0, +1). 
• When you finally take into account the spin quantum number (two options for each magnetic possibility), there are 6 possible electron states for each p orbital.

The Wave Nature of the Electron

• Planck suggested that the packages of energy followed the formula E = hv, where h is Planck's constant: 6.63 x 10^-34 Js and v is the frequency of the energy.
• Frequency is the number of waves that pass a point per second. Related to the frequency is the wavelength, how far the distance is between each crest of a wave. The shorter the wavelength, the higher the frequency. The longer the wavelength, the lower the frequency.
• If you multiple these two together, you get the speed of the wave (meters times cycles/second gives you meters/second for the wave cycles).
• Einstein solidified for us that all electromagnetic waves travel at the same speed, the speed of light, which is 3 x 10⁸ m/s, which is given the symbol c. So c = wavelength times frequency or c = λv.
• The amplitude of a wave is how high it is.
• The electromagnetic spectrum gives us the range of frequencies that electromagnetic waves can have. Radio frequencies are the longest wavelengths and lowest frequencies. Microwaves have slightly shorter wavelengths and slightly higher frequencies.
• Then there is infrared, visible light, ultraviolet, x-rays, and finally gamma rays. Gamma rays have the highest frequencies and the shortest wavelengths.