Physics 105

The Matter You Can NOT See - Atoms and Molecules

Will now look at matter more closely.  When we look more closely the first thing we learn is that all the macroscopic matter which we see with our eyes and touch with our fingers is really built up from very tiny microscopic clumps of matter bound to other clumps of matter by some force but with a great deal of empty space between clumps.  All matter looks much like our ice cube.  The differences between one piece of matter and another are to be found in the properties of the tiny clumps of microscopic matter.  We call these clumps molecules or atoms depending on the details of the structure of the clumps.

Activity: The Atom

In our first activity we will use the atom modeling kit and several spheres to make a model of an atom.  Use the atom modeling kit and yellow and red spheres to create a model of an atom. The yellow spheres represent electrons with charge -1 and mass = 1. The red spheres represent protons with charge +1 and mass of about 2000 [see Note #1]

Build an atom containing  more than 1 electron.

When you build your atom you must abide by the following two "atom" rules.

1 - The atom must contain both protons and electrons. [This is what experiments have shown]

2 - The NET or total charge of the atom must be zero. [This is what experiments have shown]

Describe your atom (words and a figure) and demonstrate that it abides by the rules.

What is the mass of your atom. What is the charge of your atom?

A force holds the proton and the electron of your atom together.  We call this force the "electrical force" (also called the Coulomb force) because it depends on the electrical charge of the particles.

The electrical force can be attractive or repulsive (pull  together or push away).  Since the atom is stable (stays together) and follows the two "atom" rules - What does your atom tell us about the conditions required for the electrical force to be an attractive force? Why?

Activity - Simple Atoms

Now, make an atom using the fewest number of protons and electrons that you can.

This atom goes by the name HYDROGEN

Describe your atom and demonstrate that it follows the two "atom" rules. What is the mass of your atom. What is the charge of your atom?  If the electron in your atom is held to the proton by the electrical force, why is the electron not pulled right down very close to the proton?

Aside: Suppose some kind person gives you $1,000,000.  Another kind person wants to increase your wealth so they give you $1 more.  Are you that much wealthier for the addition of that extra dollar?  If asked how much money you have, you might just as well say a million dollars.  That extra dollar doesn't really matter because it is so much smaller than the 1 million dollars you already had.  In the same way, suppose we have an atom with 3 protons and 3 electrons.  If some one asks what is the mass of this atom, we might say 6003.  But we could just as easily say about 6000.  This is actually more correct than 6003 in our case since the proton mass not precisely 2000!  When a number is not precise we will write it as: ~2000.  Read this number as "approximately" 2000.  Whenever we work with numbers like this we can not make the "~" go away by adding, subtracting etc.  For example, ~2000 + 4000 is ~6000 (approximately 6000) not 6000 (not precisely 6000).

Now make an atom with 1 more proton than the atom you just made.

Describe your atom and demonstrate that it follows the rules. What is the mass of your atom. What is the charge of your atom?

Your new atom is also a new ELEMENT because the number of protons determines the element. The element you have made goes by the name HELIUM.

BUT, if we look in nature for atoms like your new atom we don't find any.  It seems that although your new atom abides by the rules, it doesn't stay around very long.  Your new atom is (UNstable)!

We can find STABLE atoms with a mass essentially the same as your atom but these atoms have only one electron!

We can also find stable atoms with 2 electrons but these two electron atoms have a mass of ~6000 or ~8000.

The more massive 1 electron atom is called Deuterium (or Heavy Hydrogen) and the 2 electron atoms are called Helium3 and Helium4 depending on the mass of the atom..

Can you make a model of one of these 3 alternative atoms - mass ~4000 but with 1 electron or mass of ~6000 or ~8000 but with 2 electrons?

Notice, you can not use this mass to tell you directly how many electrons the atom contains because the mass is only approximate! 

Discuss your efforts to make this new atom..

Activity - The Neutron

Suppose the were another particle with an electrical charge of ZERO (0). We give this charge neutral particle the name Neutron.  Let blue spheres represent neutrons.

Make a model of one of Deuterium, Helium3 or Helium4 using all 3 particles, the proton, the electron and the neutron.

What can you say about the mass of this new particle using the mass of these new atoms? Discuss.

Now consider the atom you have just made. Can the same force hold all the particles in your atom together? Explain.

With electrons, protons and neutrons you can make as many atoms and "elements" as you like. Can there be different atoms of the same element?  Explain.

But there seems to be a limit to the number of elements which occur "naturally". That limit appears to be roughly around 100 protons. There may be stable elements with protons significantly above 100 but we have yet to produce one of them.

The "periodic" table below lists all the known elements. The table shows the abbreviation for the element (Al for aluminum), the number of protons (13) and a third number (26.98) roughly twice the proton number which represents a weighted average of the number of protons + neutrons in all the various forms of Al (isotopes). Notice as the number of protons gets larger this third number becomes more than simply twice the proton number.  Find a table like this table in your text book.

High Resolution Image of Periodic Table

Exercise - Find the number of protons and neutrons in the following elements: Hydrogen (H), Oxygen (O), Copper(Cu), Gold (Au).  Select 10 well chosen elements and make a graph of the number of neutrons in each element vs the number of protons in each element which represents the full range of elements in the periodic table.  What can you conclude from your graph?

Most of the chemical reactions we encounter in nature do not involve pure elements. Most chemical reactions are between molecules. A molecule is a combination of elements. With roughly 100 elements nature and man have produced a very large number of molecules.

Water is a molecule composed of 1 atom of Oxygen and 2 atoms of Hydrogen.  How many protons, neutrons and electrons are there in a water molecule? Is there just one answer to this question?

Activity - Quarks and the Color Force

Now look again at the neutron and proton in your atom. Since the electrical force can NOT hold the neutron within the atom a second force must be present to hold the neutron within the atom.  We call this force the "COLOR" force (This force has also been called the strong force).

The color force acts between particles with a "color" charge - the electron has an electrical charge but no color charge. The proton and the neutron are more complicated! The proton and neutron are NOT fundamental particles - the proton and the neutron are built from fundamental particles we call QUARKS To understand the proton and the neutron we must learn something about quarks.

Quarks have both electrical charge and color charge. There are TWO quarks of importance to us - called UP and DOWN!

The difference between the UP and the DOWN quark is the ELECTRICAL CHARGE - UP has electric charge +2/3, DOWN has electric charge = -1/3. In addition to the electrical charge, each quark must have a COLOR CHARGE either "red", "green" or "blue".

So you must replace your red and blue spheres (protons and neutrons) by quarks.

We will represent the quarks by new spheres - Up quarks will have a white swirl, DOWN quarks will have a black swirl.

Rebuild your atom replacing protons and neutrons by quarks according to the following "quark" rule: Each proton or neutron must be made up of just 3 quarks - there is more! - one quark must have a red color charge, one must have a green color charge and one must have a blue color charge.

Both the proton and the neutron have essentially a "white" or neutral color charge. The "white" charge, while neutral, still has enough "stray" color charge to bind the protons and the neutrons together into the object at the core of the atom which we call the NUCLEUS of the atom.  So the protons and the neutrons of an atom are bound to each other to for the nucleus of the atom by the small residual color force between them.

Mass of the Proton and Neutron By experiment we have found that the mass of the proton and the neutron is about 2000 times the mass of the electron as we have said.  From the quark rule, we know that the proton and the neutron are made from 3 quarks.  We might think that the mass of each quark is roughly 1/3 the mass of the proton or about 600 to 700 times the mass of the electron. 

BUT when we measure the mass of the quarks in an experiment we find that the mass of the up quark is roughly 8 times the mass of the electron and the mass of the down quark is roughly 14 times the mass of the electron.  The mass of three quarks would then be should be somewhere between 24 times the mass of the electron and 42 times the mass of the electron - not 2000 times the mass of the electron. 

Have we done something wrong or have we discovered something? 

We check and recheck our experiments and find nothing wrong - we must have discovered something!  Indeed we have discovered something very important - We have discovered that when fundamental particles are bound together there is an energy account associated with that binding - the magnitude (size) of the energy account depends on how strongly the particles are bound together (how strong the binding force is) -- and finally we have discovered that the presence of this particle binding energy account is reflected in the MASS of the bound particles.  In fact, mass itself is simply the name we give to this special energy account.  The value of mass we assign to the account is given by the equality:  Mass = Energy / c 2 .  In this equality, c is a constant (always the same).  The constant "c" is the speed of light in a vacuum.  There must be something special about light - we will come back to the question "What is special about light?" a little later in the course.

Activity - Atoms in Standard Units (kg, m, sec, coulombs)

If we think of the atom as roughly a sphere then we can ask what is the "size" or characteristic dimension of the atom.  What is the diameter of the sphere?  Experiments have shown us that in standard units of length the size (diameter) of the atom is about 1 x 10 -11 m.  If we think of the nucleus of the atom as roughly another sphere at the center of the atom then experiments have shown us that the diameter of the nucleus is about 1 x 10 -15 m.  The size of the atom is determined by the electrons and their interaction with the nucleus through the electrical force.  The size of the nucleus is determined by the interaction of the protons and neutrons, the color force.

Exercise: Given the dimensions above, if we model the nucleus of the atom as a sphere the size of a dot on this paper ( . , ~1 x 10 -4 m) how big would our model of the atom be?

What about the charge and mass of the atom and of the nucleus in standard units?  

So far we have taken the charge on the electron to be - 1.  In standard units (coulombs) the charge on the electron is -1.60 x 10 -19 Coulombs.  What is the charge on the proton in standard units?  What is the total charge of a carbon nucleus in coulombs?  What is the total charge of the carbon atom?

So far we have taken the mass on the electron to be 1.  In standard units (kg or kilograms) the mass of the electron is 9.11  x 10 -31 kilograms.  What is the approximate mass of the proton in standard units?  Approximately, what is the total mass of a carbon 14 nucleus in kg?  Approximately, what is the total mass of a carbon 14 atom in kg?

Something Else I Need To Mention:

We have treated the electrons within the atom as if they moved in simple circles - in fact the electrons within the atom are better modeled using the rules of "Quantum Mechanics". These rules give simple spherical results in special cases (a sphere is essentially the 3-Dimensional equivalent of a circle in 2-Dimensions) but more often the electrons appear to occupy regions of space which are more complex than simple spheres - some of those shapes are illustrated here.

 1 s 0              3 p 1         4 d 2        ref: http://www.orbitals.com/orb/

   

These unusual shapes are confirmed by the geometrical shapes of the molecules which are formed by combinations of atoms.

LOOK in chapter 32 of your text "The Atomic and the Quantum" if you want to learn more about Quantum Mechanics.

Do we need to understand quantum mechanics to do physics?  To consider this question, think about an old pocket watch - the kind your great grand father would have carried in his pocket - from the outside it all looks simple and straight forward - we ask how does it work -- rules: second hand goes one division per second - 60 divisions of motion - minute hand moves one minute -- 60 minutes of motion hour hand moves one hour -- that is how we tell time --- BUT if we open the pocket watch an look inside we see gears and springs - all sorts of subtle mechanisms just to produce the simple motions of the second, minute and hour hands. If we just want to tell time with a pocket watch we don't have to look inside but if we want to "build" a pocket watch we need to understand the more subtle gears and springs.  In this course we will learn how to tell time but we will not try to build a watch..

A good reference on fundamental particles can be found at: http://particleadventure.org/particleadventure/frameless/standard_model.html A good reference for the periodic table can be found at: http://pearl1.lanl.gov/periodic/default.htm A reference for the Quantum Mechanical electron patterns illustrated above can be found at: http://www.orbitals.com/orb/

A fine book on the ideas of modern physics is: Physics for Poets by Robert March ISBN 0-07-040248-5.

 

Recall the 4 Basic Concepts of the Course

ENERGY:
1 -  Nature is/has an ACCOUNTING scheme for something we know how to calculate but do not understand. We call this something ENERGY.

2 -  ENERGY has only magnitude and is always conserved. The values of individual energy accounts may change up or down but these changes must always balance.

FORCE:
3 -  FORCE is an interaction (a push or a pull) between accumulations of energy.  Force has both magnitude and direction. Force changes the value of energy accounts (increase one energy account while decreasing a second) whenever the force does WORK (acts along the direction of motion).

MATTER:
4 -  MATTER is fundamental particles which are themselves accumulations of ENERGY with certain properties.  The fundamental particles are themselves extremely small.  FORCE binds together these fundamental particles and gives matter its 3 dimensional character.

Discussion::
Identify the MATTER with which we have worked in this activity and the properties of that matter which are important for our activity.
Identify the FORCES which are important for our activity.
Identify the ENERGY ACCOUNTS which are important for our activity.

REVIEW and UNDERSTAND:

1 - The two "atom" rules.

2 - The "quark" rule and how to determine the number of quarks in an atom.

3 - The force (and is it a push or a pull) by which the electrons of the atom are bound to the nucleus of the atom.

4 - The mechanism which prevents the electrons of the atom from collapsing  to the nucleus of the atom.

5 - The force (and is it a push or a pull)  by which the protons and neutrons of the atom are held together to form the nucleus of the atom.

6 - The difference between an atom and an element.

7 - How to determine the number of electrons which make up the atom given the number of up and down quarks which make up the nucleus.

8 - How to determine the mass in kilograms of an atom given the number of up and down quarks and the number of electrons which make up the atom.

9 - How to determine the charge in coulombs of the nucleus of an atom given the number of up and down quarks which make up the nucleus

10 - What fundamental particles we have "discovered" in this activity.

11-  What energy account we have "discovered" in this activity.

12 - How the 4 basic concepts of the course apply to atoms