Chemistry - Unit 6
What do you need to know??
This chapter is on Modern Atomic Theory and it is, in some ways, a history lesson in the development of the body of knowledge surrounding the atom.
We've learned earlier, about
Democritus - 465 BC - came up with notion of atoms which he described as an elemental particle
Sir Robert Boyle - latter half of 1600s - came up with gas laws (P1V1 = P2V2), and introduced the idea that smaller particles of elements join together as molecules
Lavoisier - later half of 1700s - discovered nitrogen and is generally considered Father of chemistry
Dalton, John - (1766-1844)- The first great chemical theorist; proposed atomic theory (1807); stated law of partial pressure of gases. His ideas led to laws of multiple proportions, constant composition and conservation of mass.
Dalton's theory had four main concepts:
1. All matter is composed of indivisible particles called atoms. Bernoulli, Dalton, and others pictured atoms as tiny billiard-ball-like particles in various states of motion. While this concept is useful to help us understand atoms, it is not correct as we will see in later modules on atomic theory linked to at the bottom of this module.
2. All atoms of a given element are identical; atoms of different elements have different properties. Dalton’s theory suggested that every single atom of an element such as oxygen is identical to every other oxygen atom; furthermore, atoms of different elements, such as oxygen and mercury, are different from each other. Dalton characterized elements according to their atomic weight; however, when isotopes of elements were discovered in the late 1800s this concept changed.
3. Chemical reactions involve the combination of atoms, not the destruction of atoms. Atoms are indestructible and unchangeable, so compounds, such as water and mercury calx, are formed when one atom chemically combines with other atoms. This was an extremely advanced concept for its time; while Dalton’s theory implied that atoms bonded together, it would be more than 100 years before scientists began to explain the concept of chemical bonding.
4. When elements react to form compounds, they react in defined, whole-number ratios. The experiments that Dalton and others performed showed that reactions are not random events; they proceed according to precise and well-defined formulas.
Avogadro - right around 1800 - said that an equal volume of gas at STP contains the same number of molecules -- 6.02 x 1023 for 22.4 liters of gas.
Mendeleev - latter half of 1800s - discovered periodicity of elements and created the periodic table of elements
Thomson, Sir J.J. - 1896 - Research on cathode rays resulted in proof of existence of electrons and said that atoms were not indivisible (as Dalton had thought) but were comprised of smaller particles
Rutherford, Sir Ernest - early 1900s - Famous for his gold foil experiment that demonstrated that atoms were comprised of a dense core and the electrons were tiny and surrounded the core. Discovered half-life of radioactive elements.
We also learned about Charles (Charles' Law) a Guy-Lussac (you guessed it, Guy-Lussac's Law), but I'm leaving them out right now as we focus on the development of modern atomic theory.
As you may have already guessed, Electrons are the thing! They absolutely hold the key to understanding why substances behave as they do. So this whole lesson is on how we've learned what we've learned about electrons and how the chemists have calculated their function(s)!
From here on out in this study guide, I'm going to lead you through parsing the absolute essentials from the interesting-but-not-necessary-to-memorize bits of this topic!
This sentence is the link between electrons and quantum mechanics:
We understand electronic structure (number of electrons, where they are found in the atom and the energies they possess) from the study of light emitted or light absorbed by substances.
This is where electromagnetic radiation comes in. This radiation:
carries energy through space
includes visible light along with everything from gamma rays to radio waves with x-rays, microwaves, infrared etc. etc. included also!
ALL move through a vacuum at 3.00 x 108 m/sec (aka "Speed of light"!)
are characterized by wave-like behavior
Draw a series of waves:
Label the wavelength and the amplitude.
Now, draw a palm tree somewhere in the middle of your series of waves. Can you calculate the velocity of the wave as they pass by your palm tree? You could draw yourself in the palm tree (remember Harold and the Purple Crayon??) and count how many peaks pass by per second. Or you could use a formula. Since we know that all electromagnetic radiation moves at the same speed, we can figure out that the wavelength and the frequency (how many wave peaks passed by your palm tree in a second).
Velocity (speed of light(c) or 3.00 x 108 m/sec) = wavelength (λ) x frequency (ν)
c = (λ) (ν)
Can you rewrite this formula in terms of calculating wavelength and in terms of calculating frequency?
~ Sodium vapor lamps are used for public lighting. They give off a yellowish light with a wavelength of 589 nm (nm stands for nanometers and is equal to 10-9 meters). What is the frequency of this radiation?
The color of light depends upon the wavelengths of which it is comprised. The observed color of an object is due to the wavelengths that were not absorbed by the object. It is also dependent upon the color of light in which the object is observed. The color of light depends on the wavelengths of which it is composed. In the above example, the yellowish color of sodium vapor lamps is due to the light emitted by sodium - of a particular wavelength.
If you look at a red rose under light emitted by a sodium vapor lamp versus in the sunlight, it will appear to be different colors - this is due to the fact that the object can only reflect wavelengths of light that are being emitted by the light source!
An absorption spectrum will show only those wavelengths of light which are reflected by an object and not absorbed.
An emission spectrum will show those wavelengths of light emitted by a light source.
Different elements have different emission spectrums. That's why you can tell what gas is responsible for what color in the Northern Lights. Those electrons in each specific elemental gas emit a unique spectra -- and we see it as a unique color!
Here's a clarification of a term - intensity of light - This means the most intense wavelength of the spectrum obtained. In a band of rainbow colors that represent the emission spectrum of gases, those colors that are most prominent are of greater light intensity. And that explains why a poker stuck into a fire first becomes "red-hot", then "white-hot". (Hmmm... You want further explanation?)
The pokers are at different temperatures but made of the same elemental materials.
The pokers emit different intensities and wavelengths of electromagnetic radiation in the visible spectrum at different temperatures.
The fact that these alleged pokers do not emit intensities predicted by classical physics is what is thought of as the "ultraviolet catastrophe". The catastrophe was this: Here these scientists were thinking they were getting a handle on how light/electrons/atoms worked and then their elegant prediction failed in the real world. Catastrophe! If you were one of those scientists.
But this was important to the development of the modern atomic theory because it led to the idea that energy is quantized. That is, it is not a continuously emitted stream but rather it has a lower limit of indivisibility - a point at which it exists as a 'chunk' that cannot be broken down further. This was a revolutionary finding!
Max Planck is the scientist credited with this idea of energy quantization in 1900.
The smallest packet of light is called a quantum or photon.
The energy (E) of a quantum is related to its frequency (n) by Planck's constant (h) 6.63 x 10 -34 Joule seconds
Electromagnetic energy is always emitted or absorbed in whole number multiples of (h*n).
So, wonder of wonders, a formula was derived to allow scientists to calculate the energy of a quantum.
It is this:
Energy = Planck's Constant (h) * frequency (ν)
E = (6.63 x 10-34) (ν)
This formula allows you to calculate the value of the energy in one quantum. To calculate more than one, the right side of the equation is multiplied by (n) or the number of quanta to become:
E = (6.63 x 10-34) (ν) (n)
~ Calculate the amount of energy (one quantum) that an object can absorb from yellow light with a wavelength of 589 nm. (Remember, if you know wavelength and the speed of light, you can calculate frequency.) Also remember, the joule is the SI unit for measuring energy and = kg • m2
s2
Watch your units as you do this calculation.
The point of this formula is to explain why the intensities of light emitted do not follow the predicted model using classic physics. Planck's constant makes the difference! And demonstrates that energy is quantized.
The Photoelectric Effect
Once the chemists had this packet business figured out, they went on to wonder why, when they shined light on metals, their ammeter (a gadget that measures current or amps) showed an increased current.
Light shining on metals causes the surface to emit electrons. (Remember your physics when you learned that current is merely a flow of electrons? Hence the ammeter reading!)
For each metal, there is a minimum frequency of light below which no electrons are emitted, regardless of the intensity of light. This is called the threshold frequency, or v0
The higher the light's frequency above this minimum value, the greater the kinetic energy of the released electrons.
Since different metals have different atomic structures, the quanta of light needed to overcome the attractive forces within the atom differs for each element. It is known as the work function of the metal or Φ.
It was Einstein, in 1905, who deduced the basis of the photoelectric effect.
I like an example that Dr. Blaber, at Florida State University uses:
The Photoelectric effect as a carnival game:
"A popular carnival game is where you are given a giant mallet and have to hit a pad on the ground. This sends a small metal slug shooting up a vertical track and, if you hit hard enough, it will hit a bell at the top. This is like the photoelectric effect - the electron will be released from the atom if it absorbs a photon with enough energy. Imagine that you have a 10 year old child and Arnold Schwarzenegger. The child is too weak to hit the pad hard enough to ring the bell. It doesn't matter if you have an army of 10 year olds (intensity) lined up to take their turn - none of them will ever hit it hard enough to ring the bell. However, Arnold (being Arnold) will have no problem ringing the bell.
Thus, if a light shining on a metal does not have enough photons with the necessary energy to cause an electron to be ejected, then it does not matter how bright the light is. The key thing is to increase the energy of the individual photons, and this is achieved by increasing the frequency (i.e. decreasing the wavelength)."
We would, therefore, expect to see more electrons from atoms to be ejected, with high kinetic energy, the smaller the wavelength (and greater the frequency). And we do. X -rays are far more problematic to body tissue for example, than are radio waves! You never have to listen to a radio wearing a lead apron!
Which brings us to 1913. That's eight years after Einstein worked out the business about metals and light and electrons.
The Bohr Model
Basically, what Bohr said, in the most simplistic language, is that if the energy of electrons is quantized, then the distance from the nucleus is also quantized. His model includes these points:
He assumed that electrons were orbiting the nucleus much like planets orbit the sun.
From classical physics, a charge traveling in a circular path should lose energy by emitting electromagnetic radiation.
If the "orbiting" electrons lose energy, they should end up spiraling into the nucleus (which they do not). Therefore, once again, classical physics does not apply!
So Bohr explored the notion of quantized energy that Planck first talked about and and proposed:
that only orbits of certain radii, corresponding to defined energies, are 'permitted'
An electron orbiting in one of these "permitted" orbits:
Has a defined energy state
will not radiate energy
will not spiral into the nucleus
Bohr did a masterful job of explaining the behavior of the one electron in hydrogen. Unfortunately, it does not work for other elements.
But his work was, and is, significant in the furthering of the current understanding of atomic theory.
The Heisenberg Uncertainty Principle
There were a couple of point here:
One locates things by sight by detecting the photons that bounce off the object from a light source. And the wavelength of light used to view an object must be smaller than the object. However, the smaller the wavelength, the higher the frequency and the higher the energy of each photon. At some point, this becomes destructive. (Remember, trying to locate a cat with tennis balls??)
The Heisenberg Uncertainty Principle says that the smaller an object the greater the relative uncertainty in knowing both the position and the momentum of that object.
The point of this seemingly stray thought is that it applies to electrons. We cannot know where they are in relation to the nucleus! And we cannot think of them as moving in well-defined orbits around the nucleus, however nice that idea is.The formula that represents the principle is not something you need to memorize for this year.
The year is 1924 and a scientist named de Broglie made a daring hypothesis:
If radiant energy could, under appropriate circumstances behave as though it were a stream of particles, then could matter, under appropriate circumstances, exhibit wave-like properties?
For example, the electron in orbit around a nucleus. De Broglie suggested that the electron could be thought of as a wave with a characteristic wavelength.
Here's his formula:
wavelength = Planck's constant
momentum
OR
λ = h/mass*velocity
To complete these calculations you need to know
Planck's constant - 6.63 x 10-34 kg * m2 ;
the mass of electron - 9.109 x 10-10 kg
And you must watch your units!!!
~ What is the characteristic wavelength of an electron with a velocity of 5.97 x 106 m/s?
In 1927, Davisson and Germer proved that particles have wave properties just as de Broglie had predicted when they passed electrons through a crystal and found an interference pattern. (Have you ever sent two waves , one from each end, traveling the length of a stretched out Slinky? Sometimes the waves multiply, sometimes they cancel each other out.)
Quantum Mechanics
Let's figure out what that term means - Quantum - having to do with those tiny packets of energy that cannot be subdivided; Mechanics - how they move.
We give credit to a scientist named Schrödinger for developing an equation that incorporates both wave-like and particle-like behaviors for electrons. He worked in the latter part of the 1920s.
Since we know from the Heisenberg Uncertainty Principle that we cannot know for certain the exact location of an electron, Schrödinger describes the probability of a location of an atom.
So what we have are probability distributions for a given energy level of the electron. Electrons still have a set energy level associated with the energy of a photon, but the visualization of just where they are in relation to the nucleus has changed. Thanks to Schrödinger!
We call these areas of probable electron inhabitance "orbitals" (very different from the Bohr's "orbits" , eh?)
Schrödinger devised an equation that included three variables and places electron probability in three dimensions. His equation gives a series of wave functions that describe electron probability distributions but we are NOT going to work these out ourselves! We are going to grasp some of the implications.
Not surprisingly, the lowest energy level of the hydrogen atom calculates to be -2.18 x 1018 J - which is the same thing that Bohr calculated. Remember that his model worked for hydrogen, or for one electron, but then fell apart after that?
Schrödinger's calculated energy level also has a shape associated with it - that's the probability part. The electrons are most likely somewhere in this defined region.
Bohr defined quantum levels, saying that each level corresponded with a certain energy. In our previous calculations, n was used to denote the quantum level and could only be a positive integer.
Now, Schrödinger's model uses three quantum numbers: n, l and m1 to describe an orbital.
The principal quantum number 'n' (think energy level)
has values of 1, 2, 3, etc. (positive integers)
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