Download Date: ______ Properties of the Physical Universe: Matter Relative

Name _________________________
Date: ________
Properties of the Physical Universe: Matter
Relative Strength of Fundamental Forces
For the briefest of moments after the Big Bang, there was one force influencing the
tiny, newly spawned universe. As the universe expanded and the conditions began to
change, this ”superforce” broke down into what would become the four fundamental
forces of nature that govern our universe today. Though an exploration of the details of
each force is beyond the scope of this course, it is important to understand what forces
exist in nature, what realms of the universe they govern (see Table 5.1), and the relative
strength of the two forces (gravity and electrostatic) that we will encounter in greatest
detail.
Force of Nature
Realm of Nature
Gravity
Force that acts between objects with mass. Though it is the most far
reaching force of nature it is also the weakest of the four.
Electromagnetic
Once thought to be two separate forces (electrostatic and magnetic
force) but was shown to be one force that would exhibit different
properties based on the circumstances in question. This force is the
result of the property of tiny particles called electric charge.
Strong Nuclear
The force that governs the process of nuclear fusion where protons
and neutrons will combine under high temperatures to form new
nuclei.
Weak Nuclear
The force that dictates the fission process of heavy atomic nuclei.
There are two separate forces that act between a proton and an electron that are
separated by a short distance. A force of gravity exists due to each particle having mass.
An electrical force exists because each particle has an electrical charge. The laws used to
calculate each force are similar in form though they are quite different in nature.
Although both forces are acting at the same time, one of the forces will dominate over the
other. This exercise will demonstrate which force is the more dominant while exploring
some of the basic properties of gravitational and electrical forces. Be sure to show all
steps in your calculation and report all answers in scientific notation with three (3)
digits in the mantissa.
Newton’s Law of Gravity
FG = -
!
Coulomb’s Law
Gm1m2
r2
FE =
p+
k eq1q 2
r2
e-
!
r = 1 x 10-9 meters
Figure 5.1: A proton and an electron.
Proton Properties
Electron Properties
mp+ = 1.67 x 10 -27 kg
q p+ = 1.60 x 10 -19 C
!
!
me- = 9.11 x 10 -31 kg
q e- = -1.60 x 10 -19 C
1. Calculate the force of gravity (FG) between!the proton and electron in Figure 5.1.
!
2. Calculate the electrostatic force (FE) between the proton and electron in Figure
5.1.
3. Which of the two forces is stronger?
4. Determine how much stronger the force from question 3 is by calculating the ratio
of (FE / FG).
Nuclear Notation
The main properties of an atom are defined by the contents of its nucleus. In fact,
the type of element an atom is defined to be is dictated by the number of protons in the
nucleus. This property is called the atomic number (Z). For example, the element
Hydrogen is defined as an atom that possesses one proton in the nucleus (Z = 1) while
Helium is defined as having two protons in the nucleus (Z = 2).
Besides protons, there are neutrons inside of an atom’s nucleus. Though there is not
a specific rule as to how many neutrons can exist in the nucleus of any atom, there are
only certain numbers of neutrons (N) that have been observed to exist in atomic nuclei.
For example, hydrogen is most commonly observed to have one proton and zero neutrons
in its nucleus. In rare instances, like nuclear reactions, scientists have observed hydrogen
with a single neutron attached to the proton. This different form of the hydrogen atom is
referred to as an isotope. Isotopes exist for all of the elements observed in nature.
The mass of a neutron is only slightly larger than the mass of a proton. Because the
proton and neutron masses are nearly equal and the mass of each is vastly greater than the
mass of the electrons that surround the nucleus, the mass number (A) of an atom is
defined as the number of protons plus the number of neutrons (A = Z + N).
Elements and their nuclear properties are written in the following symbolic format:
A
Z
[X]
X ≡ Elemental symbol
A ≡ Atomic Mass: the number of protons and neutrons in the atom’s nucleus
Z ≡ Atomic Number: the number of protons in the atom’s nucleus
!
Fill in the table below by finding the chemical abbreviation, mass number and
atomic number for each element listed in the first column.
Element
Hydrogen
Helium
Nitrogen
Phosphorus
Gold
Abbreviation
Mass Number (A)
Atomic Number (Z)
Use the information provided in the first column to determine (a) the name of the
element, (b) the atomic mass, (c) the number of protons, (d) the number of neutrons.
Element Name
!
!
!
!
!
Mass Number
Number of Protons Number of Neutrons
12
6
56
26
28
14
238
92
14
7
C
Fe
Si
U
N
Atomic structure
In 1911, Ernest Rutherford proposed that the structure of an atom could be thought of
as resembling the model of the solar system where planets, comets, and asteroids are held
firmly in their orbits by a centralized force of gravity. Instead of gravity, Rutherford felt
that the attractive electrostatic force between the positively charged nucleus and the
negatively charged electrons would keep the electrons held inside tiny orbits.
A couple of years later, Neils Bohr made an important discovery about the structure
of atoms that would eventually lead physics down the road to the strange world of
quantum mechanics. In the case of the solar system, the laws of motion and gravity do
not place restrictions on the size of the orbit of any object revolving around the Sun.
Nature, as it turns out, was not so generous with the orbits of electrons inside of an atom.
Bohr discovered that most orbits would cause an electron to lose energy and spiral into
the nucleus and destroy atom. Preventing this from happening was the fact that the orbits
an electron could occupy were multiples of 0.05 nm {called the Bohr radius (rB)}
according to the relation:
& n2
r = $$
% Z
#
!! rB ,
"
where n is the orbit number (1, 2, 3…) and Z is the number of protons in the nucleus
(atomic number). This meant that the possible orbits for an electron inside of an atom
were limited in their size, which led to the notion of quantization.
Determine the size of the first three allowed orbits (n = 1, 2, 3) for a single electron
orbiting a Hydrogen nucleus (Z = 1) and a Helium nucleus (Z = 2). Calculate each
answer in units of nm and record the results in the table below.
Z
Hydrogen
Helium
n=1
n=2
n=3
With the information provided in the table above, use a drawing compass to draw the
first three orbits that an electron can have around the nucleus of Hydrogen and Helium
found in Figure 5.2. Be sure to use the scale that is provided in order to draw in the sizes
of each orbit accurately.
Figure 5.2
Hydrogen
p+
0 nm
0.25 nm
0.50 nm
Helium
2p+
0 nm
0.25 nm
0.50 nm
Due to the attractive nature of the electrostatic force, the electron will have a
tendency to reside in an orbit that is as close to the nucleus as possible. If an atom is
moving with little energy, as is the case of atoms in a cool cloud of gas, then the electron
in a given atom will find itself in the orbit that is closest to the nucleus (n = 1). In this
case, the atom is referred to as being in the ground state. If the gas is heated, the
vibration of the atoms in the gas will increase causing some of the energy to be absorbed
by the electron orbiting the nucleus. When this occurs the electron can be forced to move
to an orbit that is further away (n = 2, 3…) from the nucleus. When an electron makes
such a transition, the atom is then referred to as being in an excited state.
Binding Energy
Binding energy is the amount of energy an electron has while it orbits the nucleus.
Since the possible orbits inside an atom must be of specific sizes, the corresponding
binding energies must have specific values (multiples of the Rydberg Energy). To
simplify the following exercise, we will focus on the binding energy of a single electron
orbiting the nucleus of an atom. In doing so, the binding energy of an electron will only
depend on the atomic number (Z) and the orbit number (n) that the electron is found.
(1) Determine the binding energy for a single electron that is found in the first six (n = 16) orbits of an atom of Hydrogen (Z = 1), using the following relation:
& Z2
B.E. = $$ 2
%n
#
!! (-13.6 eV)
"
Show all work in your calculation and record the results in the table below.
Report your answers in units of electron-Volts (eV). {Note: 1 electron-Volt is
equal to 1.60 x 10-19 Joules}.
Hydrogen
n=1
n=2
n=3
n=4
n=5
n=6
Binding Energy
Chemical Notation
Besides mass, the most basic property of the particles that make up an atom is
electrical charge. The proton and electron each have an electrical charge that is equal in
quantity but opposite in sign. In its most simplified terms, the proton is considered to
have a charge of positive one (+1) and the electron a charge of negative one (-1).
Neutrons have zero electrical charge and are considered neutral.
Under typical conditions, atoms have the same number of protons and electrons
making the atom electrically neutral. Under some conditions, like high temperatures,
electrons can become torn away from the atom. In such cases, the atom will be left with
more protons than electrons, which will give the atom a net positive charge. In other
instances, extra electrons can be added to the atom giving the atom a net negative charge.
In either case the atom is considered ionized. The ionization level of any atom refers to
the total net charge (positive or negative) that exists due to the release or addition of
electrons, and is commonly written at a superscript after the elemental symbol (e.g.
Hydrogen with one missing electron would be written as, H1+).
[X ]
I
I ≡ Ionization Level: number indicates whether there are missing electrons (positive
number) or extra electrons (negative number) orbiting the nucleus
Write out the abbreviations for the list of atoms with the given ionizations.
Ionized Atom
!
Symbolic Abbreviation
Hydrogen with one (1) extra electron
Carbon with two (2) missing electrons
Oxygen with two (2) extra electrons
Helium with one (1) extra electron
Iron with four (4) missing electrons
Due to the arrangements of electrons surrounding the nucleus, atoms are able to
combine through the sharing or exchange of the electrons to form different molecules.
Molecular complexity ranges from being as simple as the combination of two of the same
element (e.g. O2 ≡ oxygen) to the combination of dozens of elements (e.g. C6H12O6 ≡
glucose). The subscript that follows each elemental symbol refers to the number of that
particular atom that exists in the molecule.
[ X ]M
M ≡ indicates the number of atoms that are part of a given molecule
Fill out the table below with (1) the names of the elements that make up each
molecule, (2) the number of each element in the molecule, and (3) the common name for
each molecule.
!
Molecule
O3
H 2O
!
!
!
!
!
CO 2
SiO 2
C 6H12O 6
Molecular Name
Name and number of each element in the molecule