The Atom: Quantum Mechanical Model

Born, Planck, Heisenberg and Schrondinger built on the work of Rutherford to develop the Quantum Mechanical Model of the Atom.  Here are the primary points:

1. Energy is ultimately quantized into small discrete packet that we call photons.
2. Electrons can absorb (gain) or emit (lose) photons, but they can't use or lose a portion of a photon.
   - When an electron gains/absorbs a photon it will become excited and jump to a higher energy level.
   - When an electron loses/emits a photon it will has less energy and jump to a lower energy level.
   - Electrons DO NOT MOVE (Newtonian concept), they JUMP.  They cannot use a portion/fraction of a photon.  It's all or nothing.
   - When electrons jump from one energy level to another, it is called a Quantum Leap.  They have gained or lost a quantized amount of energy- a photon.
3. Heisenberg Uncertainty Principle- (basic) The exact velocity and location of an electron cannot be determined without changing its velocity and/or location.  We can only determine an electron's probable location in the electron cloud.  This probable position is explained by the 4 Quantum Numbers.
4. Quantum Numbers
• Principle Quantum Number describes the distance from the nucleus, or the energy level.
• Orbital Quantum Number describes the shape of the electron cloud.
• Magnetic Quantum Number describes the orientation of the electron cloud in space with respect to the 3 axis.
• Spin is a notation of up/down to represent that the electrons within a pair will always be as far apart as possible (Remember- like charges repel).
5. Pauli Exclusion Principle- No 2 electrons in the same atom can have the same 4 Quantum Numbers.  A pair of electrons in the same atom will be in the same energy level, shape and orientation, but they will always be as far apart as possible.

The Atom: Development of the Modern Theory

In 1897 British physicist Joseph John (J. J.) Thomson (1856–1940) discovered the electron in a series of experiments using a cathode ray tube at Cambridge University.  He said that there were "bodies much smaller than atoms" that had a negative charge.  He called the negative particles electrons. Thomson took the model of the atom one step further with his plum-pudding model.  While you might not be familiar with plum-pudding, you are probably very familiar with a chocolate cookie.  Thomson theorized that if there were negative particles in the atom, there must also be a positive charge to make an atom neutral. His model described the atom as being basically positive (the cookie) with areas of negative that can be broken off (the chips).

One of Thomson's students, Ernest Rutherford built on his research and further developed our modern concept of the atom. One of his first discoveries was that radiation was not a single substance but three. While he was at McGill University in Canada, he found that radiation could be influenced by an electrical charge.  The radiation that was attracted to a negative charged, he called alpha (positive charge).  The radiation that was attracted to a positive charge he called beta (negative charge).  Later gamma radiation was found to be unaffected by any charge (neutral).

After receiving the Nobel Prize, Rutherford moved to Manchester and attracted many young scientists to his research group. Under his direction, they continued to study the atoms and radiation.  The Gold Foil Experiment was to become one of the most famous.  In this experiment, alpha particles (+) were fired at a very thin sheet of gold foil.  It was expected that the particles would go straight through the foil like bowling balls through tissue paper.  Imagine their surprise when some of the particles seemed to be deflected, and even bounced back off.  This observation led to the conclusion that the atom is mostly empty space, with a small, hard positively charged center.  Rutherford called this the nucleus.  This group would go on to discover the proton in 1917.

Later Rutherford and a fellow Danish physicist, Neils Bohr, developed a new model of the atom.  They were bothered by the concept that if electrons were small and negative, and the nucleus was dense and positive, why don't the electrons simply fall into the nucleus?  They developed a model that described the atom as having a small positive nucleus with the electrons orbiting the nucleus in energy levels.  In this model, the electrons are held in the atom by the electrostatic attraction between the positive nucleus and negative electrons, but are constantly being pushed outward by their angular momentum.  This is the familiar planetary model that is commonly taught to young students.

During this same time, Max Planck was studying electromagnetic radiation in Berlin. Among his many discoveries, he found that EMR is quantized. That it is carried by small, discrete packets that he called photons. These small quantities cannot be divided, they are the smallest amount of energy.  This can be very difficult for us to conceptualize.  We live in a world where we can divide amounts easily into smaller amounts.  You don't have to use an entire gallon of gas at a time, you can just use a little, then a little more.  But when you start to look at the world on the subatomic level, you reach a point where it is all or nothing.  Think of money.  We normally think in terms of dollars.  That's the level we are comfortable with, that we use everyday. Dollars can be broken down into quarters, dimes, nickels and even pennies.  We don't think of paying for everything in pennies because they are very small in relation to what we are buying- but imagine buying something very small. Can you pay for something worth a portion of a penny?  No, you either use a whole penny or not.  Photons are the pennies of the electromagnetic spectrum.

Bohr and Rutherford incorporated this concept into their model. Now an electron could not move from one level to another, it had to jump or make a quantum leap. When an electron absorbs a photon, it will jump to a higher energy level, when an electron emits a photon, it will fall to a lower energy level.  Again, this is difficult for us to imagine.  We think in terms of something orbiting, but in reality electrons don't orbit, they jump. 

Werner Heisenberg, Max Born and Wolfgang Pauli took these ideas and formed the quantum mechanical model of the atom.

The Atom: Early Theories

The modern concept of the atom can be traced back to Democritus in 465 BC.  Unlike most Greeks of his time, he believed that everything was made up of small, indivisible shapes that he called atomos.

For the next 2 thousand years, most thinkers, philosophers and alchemists followed the basic idea set down by Aristotle.  He argued that everything was composed of some combination of the 4 elements- fire, earth, air and water.  This belief slowly began to break down during the Renaissance. This was when belief and debate began to be replaced with experimentation and observation.

Antoine Lavoisier (1743-1794) began to pull the ideas of the previous 200 years when he clearly stated the Law of Conservation of Matter.  From his experiments, he found that even if the appearance of a substance may change, the total mass of the materials before a change will always equal the total mass after the change. Thanks to Einstein, we now realize that we can make nuclear changes that will convert matter into energy, but Lavoisier's concept is still valid for chemical changes.
Law of Conservation of Matter- matter can neither be created nor destroyed by ordinary chemical means.

In the early nineteenth century, Dalton further defined matter by clearly stating that all matter is composed of atoms. He said an atom is the smallest unit of an element that can exist alone or in combination with other atoms of the same or different elements.

1. All matter is made up of very small particles called atoms.
2. Atoms of the same element are all chemically alike: atoms of different elements are chemically different.
3. The atoms of different elements have different average masses.
4. Atoms are not subdivided in chemical reactions, they unite in simple ratios to form compounds.

Over the next century, many others made contributions to our concept of the atom. Many different types of atoms (elements) were identified and investigated.  By the end of the nineteenth century, about 60 elements had been discovered and described.  Dmitri Mendeleev was the first to publicly attempt to organize the elements and look for patterns.  He organized the known elements by atomic weight and their known properties.  He was even able to predict the properties and atomic weights of elements that had not been discovered yet, but there were problems with his table.  There were several elements that seemed to be in the wrong place.  One of the most glaring was iodine.  Iodine clearly had properties similar to bromine, but it fell in the same row with oxygen.

Henry Gwyn Jeffreys Mosley (1887-1915):  Mosley began to work on the inconsistencies found in Mendeleev's table at Oxford. He arranged the elements in order of their atomic numbers horizontally and formed columns of elements with similar properties. Tragically for the development of science, Moseley was killed in action during WW1 at Gallipoli in 1915. 

The modern periodic law states that if the elements are arranged by increasing atomic number, their properties will reoccur at regular intervals.

The Atom: Isotopic Notation

Isotopes are atoms with the same number of protons but have a different number of neutrons.  They are basically different varieties of the same element.  Two of the most common isotopes that people hear about are Carbon-14 and Carbon-12.  Both isotopes are carbon because they each have 6 protons.  They are different because C-14 has 8 neutrons and C-12 only has 6.  While C-12 is the most abundant (common) isotope of carbon, both are called isotopes.

The number of protons in an atom is also called the atomic number.  The number of protons determines the identity of an atom, no matter how many neutrons or electrons are in the atom.  Atomic number is listed on the periodic table.  It is a whole number and is usually listed above the symbol for the element.  If you change the number of protons in an atom, the element has also changed.

Mass number is the total number of particles in the nucleus of an atom.  In other words, it is the number of protons plus the number of neutrons.  Isotopes have the same atomic number, but different mass numbers.  Mass numbers are NOT listed on the periodic table.  When you name a specific isotope, you MUST include its mass number, for instance Carbon-14 or Uranium-135.

The number below the symbol of the element on the periodic table is called the atomic mass.  It is the weighted average mass number of all the isotopes of a particular element.  Because it is an average, it has significant digits.

We can represent an isotope in an abbreviated form.  This is called the isotopic notation.

Here is the isotopic notation for carbon 14.

From looking at the isotopic notation, you can determine the number of protons, neutrons and electrons for a given atom.

In a neutral carbon 14 atom, determine the number of protons, neutrons and electrons?
Protons- The atomic number is 6, therefore there are 6 protons
Electrons- If the atoms is neutral the number of protons equals the number of electrons, therefore there are also 6 electrons.
Neutrons- The mass number equals the number of protons + neutrons, therefore 14-6 leaves 8 neutrons.

Mixtures

Pure substances are uniform throughout with a definite composition and properties, while mixtures are physical combinations of two or more pure substances. The properties of the substances in a mixture retain their own properties.

We can further divide pure substance in chemistry into elements and compounds.  An element is basically the name of a type of atom defined by the number of protons in the nucleus.  A compound in a chemical combination of two or more elements.  A compound is the name of a type of molecule (chemically bonded atoms).

Note:  Physical combination means that substances are just dispersed or close together. A chemical combination means that the atoms are chemical attached creating new molecules with new properties.  Chemical bonds cannot be separated by physical means.

Mixtures can be divided into homogeneous mixtures that appear to be a single substance and heterogeneous mixtures that are obviously two or more substances.

All mixtures are composed of a solute and a solvent. The solute is the substance that is dissolved or dispersed, while the solvent is the substance that does the dissolving.  The solvent separates and keeps the solute particles apart.

Mixture can be divided into three categories:

Solutions are homogeneous and clear.  The particles are so small they cannot be seen and do not reflect light.

     Ex:  windex, tap water, air

Colloids are homogeneous but appear cloudy.  Some of the particles are large enough to reflect light even though they can’t be seen with the naked eye.

     Ex:  milk, fog, mayonnaise

Suspensions are heterogeneous.  Given time gravity will separate a suspension with the most dense particles on the bottom, and the least dense (lightest) particles rising to the top.

     Ex:  Italian salad dressing, oil and water

Describing Matter

In lab we make both qualitative and quantitative measurements.  We can further describe matter in terms of extensive and intensive properties.  Extensive properties are quantity specific, such as mass and volume. The mass of a sample of water depends on how much water you have in a sample. Intensive properties are dependent only on the type of matter, not the quantity.  The density of water is 1.0 g/mL whether you have a drop or a swimming pool full.

We can further divide observations into physical and chemical properties.  Physical properties describe matter without changing its composition.  Chemical properties describe how matter interacts or changes with other matter.

Physical Properties                                Chemical Properties

Color                                                                Rusting

Odor                                                                 Burning

Density                                                            Tarnishing

Boiling Point

Malleability

The state of matter, and its boiling and melting points are all physical properties.  The state of matter is determined by the arrangement of its particles.

The change of state of a substance is a physical change.

                                    Boiling                                                Evaporating

                                    Melting                                               Condensing

                                    Freezing                                              Sublimation

                                    Solidifying

If the identity of a substance is changed, or a new substance is formed, it is a chemical change.

Unit Analysis: Density

You must use unit analysis to solve density problems in chemistry (NOT THE FORMULA & ALGEBRA).  Remember you are learning the process  of unit analysis, not simply finding the correct answer!

Use the technique you have learned in problem solving:  what are you looking for, what are you given, put the units together to cancel and solve.

Example #1

A sample of a known metal is dropped into a graduated cylinder with 25.0 mL of water. The level rises to 31.5 mL. If the given density of the metal is 2.56 kg/L, what is the mass of the sample in grams?

Possible Questions
Where did 6.5 mL come from? A substance displaces its volume when immersed in water.  The water level rose from 25.0 to 31.5 mL.
Why are there only 2 sig dig in the final answer?  When you multiply and divide, you use the least number of sig dig.  2.56 kg/1L has 3, 6.5 mL has 2, and the conversions for L and kg are exact values with an infinite number of sig dig.


Example #2

What is the volume of a sample of aluminum in L that weighs 56.7 g?  The density of aluminum is 2.71 g/mL.

Possible Questions

Why flip the density?  To make sure the units of volume will be in the numerator.

I got a different answer (0.153657), why? Remember that 2.71 is in the denominator.  You must divide, not multiply. You can either input 56.7 first, divided by 2.72, divided by 1000
OR start with 1 divided by 2.71, times 56.7, divided by 1000.

Unit Analysis: Solving Word Problems

Unit Analysis can make solving complex word problems much easier.  First, DON’T BE INTIMIDATED!  The problem is not going to jump off the page and bite you if you get it wrong!  Just TRY!  Follow these basic steps to simplify problem solving.

1. What are your looking for?  Read through the problem and determine the exact units requested.

          WRITE THAT DOWN!

2. What are you given?  Sometimes, there is so much information given it is a good idea to write it all down or underline it in the problem.  It also helps if you will label what type of given information it is.  For instance:  mass, distance, …

3. Is there any other information you need?  Conversions, molar mass, reactions, …

4. Put the units together in such as way that you cancel out the units you don’t want and end up with only the units requested.  If the units are reversed in your final answer, just flip your calculation.

Example #1

A farmer has 2 cows and he decides to change to chickens.  He can barter 4 emu for each cow, 3 emu for 5 pigs, 8 pigs for 3 llama,  a llama for 20 rabbits and 3 rabbits for 2 chickens.  How many chickens can he get for both his cows?

1. What are you looking for?  chickens

2. What are you given?  Many ridiculous ratios with animals.

3. Is there any other information needed?  Not for this problem, just watch out where you step.

4. Use UA to determine the units requested.

When you plug these values into the calculator, the screen reads 66.66666667, but we are looking for WHOLE, LIVE chicken, not parts.

Remember that in science we deal with objects and measurements, NUMBERS HAVE MEANING.  You must evaluate your answer based on what the units are, as well as significant digits.

Example #2

A machine produces 4.5 x 10³ m of spaghetti noodles each minute. A package of noodles contains 128 noodles that are each 12.5 inches long.  The company sells the noodles in cartons containing 20 packages for $75.50.  If the machine runs 12.0 hr a day, 5.00 days a week, 50.0 weeks a year, how much money can the company make each year from that one machine?

Unit Analysis: The Basics

Unit analysis or dimensional analysis is a method used to calculate values based on the units of each measurement.  We will start by using this method to simply convert one measurement in one unit to another unit. This technique may seem more complicated than necessary at this point, but remember you are learning how to use the units.  Later in the semester you will see that unit analysis will make problem solving so much easier!

Unit analysis is based on two very fundamental mathematical principles.

1. any number multiplied by one is equal to itself
2. a fraction equals one if the value of the numerator equals the value of the denominator

These two properties allow us to let the measurements determine how to do the calculation.  The final answer must have the units desired and all other units must be canceled.

Changing both the unit in the numerator and the denominator is just like changing only one set of units.  Just remember that all the units except the ones needed must cancel.

Change 3.40 m/sec to km/yr.

Notice that you must put the 60 sec in the numerator to cancel the sec you were given.  All units must cancel except the ones requested in the problem.  In this case, km/year.