Electron Arrangement in Atom 1. Historic Basis 2. Modern Theory 3. Three Quantum Numbers as Locators LECTURE Fifteen CHM 151 ©slg Topics:

WHERE THE ELECTRONS ARE..... We are going to examine in historical succession the ideas and experiments that led to the modern atomic theory and sophisticated placement of the electrons about the nucleus. The current theory, based on quantum mechanics, places the electrons around the nucleus of the atom in “ORBITALS,” regions corresponding to allowed energy states in which an electron has about 90% probability of being found.

Historical Events, Nature of Electromagnetic Radiation James Maxwell: Wave motion of electromagnetic radiation Rydberg, Balmer: Wavelength of atomic spectra Max Planck: Quantum theory of radiation, packets of specific energy 4. ~1905 Einstein: Particle- like properties of radiation, “photons”

James Maxwell described all forms of radiation in terms of oscillating (wave like) electric and magnetic fields in space. The fields are propagated at right angles to each other. All “forms of radiation” include visible light but also, x-rays, radioactivity, microwaves, radio waves: all are described today as electromagnetic radiation. The waves have characteristic frequency and wavelength, and travel at a constant velocity in a vacuum, 3.0 X 10 8 m/s.

Wave description: Frequency: # cycles / sec

c = speed light, vacuum = wavelength X frequency 3.00 X 10 8 ms -1 =, m X, s -1 (hertz) hertz, Hz, s -1 # cycles per second Same as m/s = c/ = c/ Important Relationship, all electromagnetic radiation: Rearranging:

A red light source exhibits a wavelength of 700 nm, and a blue light source has a wavelength of 400 nm. What is the characteristic frequency of each of these light sources? Red light: 700 nm = ? m = ? s nm 1m = 700 X m = 7.00 X m 10 9 nm = c / = 3.00 X 10 8 ms -1 = 4.29 X s X m = 4.29 X cycles per sec = 4.29 X Hz or s -1

Blue Light: 400 nm = ? m = ? s nm 1m = 400 X m = 4.00 X m 10 9 nm = c / = 3.00 X 10 8 ms -1 = 7.50 X s X m = 7.50 X cycles per sec = 7.50 X Hz

RED light: 700 nm, 4.29 X Hz BLUE light: 400 nm, 7.50 X Hz Point to remember: the shorter the wavelength, the higher the frequency: the longer the wavelength, the lower the frequency. longer lowe r shorter higher

GROUP WORK Microwave ovens sold in US give off microwave radiation with a frequency of 2.45 GHz. What is the wavelength of this radiation, in m and in nm? = c/ 2.45 GHz = ? m = ? nm 10 9 Hz (s -1 ) = 1 GHz c = 3.00 X 10 8 ms Convert GHz to Hz; call Hz “s -1 ” 2. Calculate wavelength,, in m 3. Convert m to nm (10 9 nm = 1 m)

Max Planck made a major step forward with his theory that energy is not continuous but rather is generated in small, measurable packets he called quantum (which refers back to the Latin, meaning bundle). He related the energy of the quantum to its frequency or wavelength as below: Energy quantum = h x radiation = h x c radiation h is Planck’s constant, 6.63 X joule sec

c, speed of light = Wavelength, X frequency, = c = c Wavelength, frequency, energy relationships: energy of photon = h, Planck’s constant x E = h = h c higher shorter

Sample Calculations: E = h = h c Blue light, = 4.00 X m E = 6.63 X joule s x 3.00 X 10 8 ms X m E = 4.97 X joule Microwave oven, = 2.45 X 10 9 Hz or s -1 E = 6.63 X joule s x 2.45 X 10 9 s -1 E = 1.62 X joule

The relationships expressed by this equation include the following: Energy of a quantum is directly proportional to the frequency of radiation: high frequency radiation is the highest energy radiation (x rays, gamma rays) Energy of radiation is inversely proportional to its wavelength: long waves are lowest in energy, short waves are highest. Radio waves, microwaves represent low energy forms of radiation. View CD ROM sliding spectra here

Einstein took the next step in line by using Planck’s quantum theory to explain the photoelectric effect in which high frequency radiation can cause electrons to be removed from atoms. Einstein decided that light has not only wave- like properties typical of radiation but also particle- like properties. He renamed Planck’s energy quantum as a “photon”, massless particles with the quantized energy/frequency relationships described by Planck. “Quantized” refers to properties which have specific allowed values only.

It was discovered in this time frame that each element which was subjected to high voltage energy source in the gas state would emit light. When this light is passed through a prism, instead of obtaining a continuous spectrum as one obtains for white light, one observes only a few distinct lines of very specific wavelength. Each element emits when “excited” its own distinct “line emission spectrum” with identifying wavelengths. The discovery of emission lines led to calculations relating their wavelengths by both Johann Balmer and Johannes Rydberg. Class view spectra here....

Historical Events, the Nature of Electron Dalton: Indivisible atom Thomson: Discovery of electrons Thomson: Plum Pudding atom Rutherford: The Nuclear atom Bohr: Planetary atom model, e’s in orbits

JJ Thompson’s Picture of the atom:

Rutherford’s Picture of the Atom:

Bohr combined the ideas we have met to present his “planetary” model of the atom, with the electrons circling the nucleus like planets around the sun:

Bohr used all the ideas to date: electron in the atom outside the tiny positive nucleus excited elements emit specific wavelengths of energy only radiation comes in packets of specific energy and wavelength Bohr’s atom placed the electrons in energy quantized orbits about the nucleus and calculated exactly the energy of the electron for hydrogen in each orbit.

Bohr also predicted that each shell or orbit about the nucleus would have its occupancy limited to 2n 2 electrons, where n = the orbit number. Many of Bohr’s ideas, in modified form, remain in the present day quantum mechanics description of atomic structure. Bohr was able to calculate exactly the energy values for the hydrogen spectrum using his model; however the calculations only worked for one electron systems and did not explain the electronic behavior of larger atoms.

GROUP WORK Predict maximum occupancy (2n 2 )of each shell: n=1 = _____ e’s n=5 = _____ e’s n=2 = _____ e’s n=6 = _____ e’s n=3 = _____ e’s n=7= _____ e’s n=4 = _____ e’s

Planck Energy is “quantized”, comes in packets with energy hv Einstein Energy can interact with matter, photoelectric effect, “photon” Bohr Photons of energy can interact with electrons in orbits of lowest possible energy around the nucleus and “excite” e’s to higher energy orbits. The e’s give off this energy as light, spectral lines as they return to “ground” state. Summation:

Electron as matter/energy particle DeBroglie: Matter Waves Heisenberg’s Uncertainty Principle Schroedinger’s Wave Equation and Wave Mechanics 4. Modern Theory: Use of wave equation to describe electron energy/probable location in terms of three quantum numbers.

DeBroglie next suggested that all matter moved in wavelike fashion, just like radiation. Large macroscopic matter (moving golf balls, raindrops, etc) have characteristic wavelengths associated with their motion but the wavelengths are too tiny to be detectable or significant. Electrons, on the other hand have very significant wavelengths in comparison to their size. Einstein gave radiation matter- like, particle properties; DeBroglie gave matter wave- like properties.

Heisenberg’s Uncertainty Principle: If an electron has some properties that are wave like and others that are like particles, we cannot simultaneously describe the exact location of the electron and its exact energy. The accurate determination of one changes the value of the other. The Bohr atom tried to describe exact energy and position for the e’s around the nucleus and worked only for H.

Born’s interpretation of Heisenberg’s Principle: If we want to make an accurate statement about the energy of an electron in the atom, we must accept some uncertainty in its exact position. We can only calculate probable locations where an electrons is to be found. Schroedinger’s wave equation describes the electron as as a moving matter wave, and results in a picture in which we place electrons in probable locations about the nucleus based on their energy.

Schroedinger’s Wave Equation The mathematics employed by Schroedinger to describe the energy and probable location of the electron about the nucleus is complex and only recently been solved for larger atoms than hydrogen. However, it yields a description of the atom which accounts for the differences between the elements. IT WORKS!

Schroedinger’s wave equation describes the electrons in a given atom in terms of probable regions of differing energies in which an electron is most likely to be found. We call the regions “orbitals” rather than “orbits”, and each is centered about the nucleus. The description of each orbital is given in the form of three “quantum numbers”, which give an address like assignment to each orbital. The quantum numbers are in the form of a series of solutions to the wave equation.

Heisenberg: Uncertainty Principle: cannot determine simultaneously the exact location and energy of an electron in atom Schroedinger: Wave equation to calculate probable location of e’s around nucleus using dual matter/wave properties of e’s. Three quantum numbers from equation locate e’s of various energies in probable main shells, subshells, orbitals. Summation:

The Quantum Numbers “Locators, which describe each e - about the nucleus in terms of relative energy and probable location.” The first quantum number, n, locates each electron in a specific main shell about the nucleus. The second quantum number, l, locates the electron in a subshell within the main shell. The third quantum number, m l, locates the electron in a specific orbital within the subshell.

“n”, the Principal quantum number: Has all integer values 1 to infinity: 1,2,3,4,... Locates the electron in an orbital in a main shell about the nucleus, like Bohr’s orbits describes maximum occupancy of shell, 2n 2. The higher the n number: the larger the shell the farther from the nucleus the higher the energy of the orbital in the shell. Locator #1, “n”, the first quantum number

Locator #2, “l”, the second quantum number locates electrons in a subshell region within the main shell limits number of subshells to a value equal to n (1 in 1st shell, 2 in 2nd shell, 3 in 3rd shell etc) only four types of subshells are found to be occupied in unexcited, “ground state” of atom These subshell types are known by letter: “s” “p” “d ” “f”

n = 1 n = 2 n = 3 n = 4 n = 5 n = 6 n = 7 1s 2s 2p 3s 3p 3d 4s 4p 4d 4f 5s 5p 5d 5f (5g) 6s 6p 6d (6f 6g 6h) 7s (7p 7d 7f 7g 7h 7i) Lowest energy, smallest shell Highest, biggest

And More About “l”: AS WELL AS LOCATION, this Q# is quite important in describing a relative energy value for each of these regions, and the shape of each orbital in the subshell. We will see shortly that each subshell type, s, p, d, f contain orbitals of unique shape. The “l” Q# distinguishes between the subshells in terms of energy, s <p <d <f

Locator #3, “m l ”, the third quantum number “m l ”, the third quantum number, specifies in which orbital within a subshell an electron may be found. It turns out that each subshell type contains a unique number of orbitals, all of the same shape and energy.

This third number completes the description of where a electron is likely to be found around the nucleus: All electrons can be located in an orbital within a subshell within a main shell. To find that electron one need a locating value for each: the “n” number describes a shell (1,2,3...) the “l” number describes a subshell region (s,p,d,f...) the “m l ” number describes an orbital within the region

The Third Q #, m l continued “m l ” values will describe the number of orbitals within a subshell, and give each orbital its own unique “address”: s subshell p subshell d subshell f subshell 1 orbital 3 orbitals 5 orbitals 7 orbitals

Now that we have found places to put our electrons, in orbitals within subshells within shells, let’s take a look at the shapes of the various types of orbitals. The “orbital shapes” are simply enclosed areas of probability for an electron after a three dimensional plot is made of all solutions for that electron from the wave equation. Each orbital within a subshell is centered about the nucleus and extends out to the boundaries of its main shell. Its exact orientation within the subshell depends on the value of its m l number.

“To be continued...”