Download Mass Defect (not in book)

Unit 2 – Chemical Foundations and Nuclear Chemistry
Chapter 3 –Chemical Foundations: Elements, Atoms, and Ions
The Elements
The early Greeks thought the universe was made of only four elements: air,
earth, fire and water. Today we know of over 100 different elements, from which
millions of known substances are composed of. Just like the alphabet, with its 26
letters, can be used to construct many different words, the elements of the
periodic table can be used to construct an almost infinite number of compounds.
Dalton’s Atomic Theory
John Dalton (1766-1844) was a school teacher who also conducted scientific
experiments on the side. In the early 1800’s, some basic ideas about matter
were generally accepted by scientists:



Most natural materials are mixtures of pure substances.
Pure substances are either elements or combinations of elements.
A given compound always contains the same proportions by mass of the
elements.
John Dalton took these ideas and formalized them into his now-famous Dalton‘s
Atomic Theory:
1) All elements are composed of tiny particles called atoms.
2) Atoms of the same element are identical.
3) The atoms of a given element are different from those of any other
element.
4) Atoms of one element can combine with atoms of other elements to
form compounds.
5) Atoms are indivisible in chemical processes. A chemical reaction
simply changes the way the atoms are grouped together.
Subatomic Particles
We now know that some of these ideas have proved to be incorrect. For
example, when the neutron was discovered by James Chadwick in 1932 gave
rise to the concept of isotopes (atoms of the same element that differ in the
number of neutrons in the nucleus). The basic subatomic particles are given in
the table on the next page.
particle
symbol
charge
mass (amu)*
location
electron
proton
neutron
ep+
no
-1
+1
0
1/1840
1
1
e- cloud
nucleus
nucleus
*1 amu = 1.66 X 10-24 g
The first subatomic particle discovered was the electron. In the late 1890’s, J.J.
Thomson set up a cathode ray tube and hooked it up to a battery. The resulting
stream of electrons excited the gas particles in the tube and caused it to glow.
EX: Draw a schematic of a cathode ray tube below:
It was discovered by Ernest Rutherford that the protons and neutrons were
located in a very small region called the nucleus. This experiment was done by
shooting some positively charged  particles at some gold foil.
EX: Draw a schematic of Rutherford’s famous gold foil experiement.
Atomic Number
The atomic number (sometimes given the symbol “Z”) is the number of protons in
the nucleus. This number is what gives an element its identity. For example,
any atom with 6 protons in its nucleus is carbon. The periodic table is arranged
in order of increasing atomic number.
Mass Number
Atoms of the same element can differ in the number of neutrons in the nucleus.
Such variations lead to isotopes, which have the same number of protons, but
different numbers of neutrons. The mass number of an atom is the number of
protons + the number of neutrons the atom has.
EX: What is the mass number of a carbon atom that has 5 neutrons in its
nucleus?
EX: How many nuetrons will a calcium atom have if its mass number is 42?
To symbolize an isotope, we can use the following notation:
mass number
mass number
atomic number
atomic number
The atomic number is redundant information, and is sometimes left off. For
example, the “2” shown above for helium is unnecessary, since all helium atoms
have two protons.
We name an isotope by writing the element name followed by a dash and then
the mass number. The above examples would be called helium-4 and helium-5,
respectively. The only exception to this would be hydrogen. Hydrogen-1 is
sometimes called just “hydrogen”. Hydrogen-2 is sometimes called “deuterium”
and hydrogen-3 is sometimes called “tritium”. (Most hydrogen found in nature is
hydrogen-1.)
EX: Write the symbol and determine the number of neutrons for a gold-197
atom.
FYI- an “amu” is 1/12 the mass of a carbon-12 atom. Amu stands for atomic
mass unit and is equal to 1.66 X 10-24 g.
Atomic Mass (not in book)
Each isotope of each element exists in nature in different abundances. The
atomic mass is the weighted average of all the isotopes of that element. For
example, about 99% of all carbon atoms are carbon-12. About 1% are
carbon-13. Thus, the weighted average is somewhere between 12 and 13 amu.
Since carbon-12 is much more abundant, the average is shifted closer to 12 than
to 13. A periodic table shows that carbon has an atomic mass of 12.011 amu.
EX:
What would you guess is the most common isotope for Scandium?
What would its symbol be, and how many protons, neutrons, and
electrons would it have?
Calculating Atomic Mass
EX:
The element copper is found to contain the naturally occurring isotopes
Cu-63 and Cu-65. Their abundance is 69.17% and 30.83%, respectively,
and their masses are 62.9296 amu and 64.9278 amu. Calculate the
atomic mass for copper.
EX:
Neon has three isotopes with the % abundance and mass given for each.
Use this information to calculate the atomic mass of neon.
isotope
Neon-20
Neon-21
Neon-22
mass (in amu)
19.992
20.994
21.991
abundance
90.48 %
0.27 %
9.25 %
Mass Spectroscopy
The basic principle behind this technique uses a magnetic or electric field to
deflect charged cations. The heavier cations are deflected less than the lighter
cations, and a counter measures the relative amount of each isotope. The basic
steps are:
1) Vaporize a sample of matter by heating it.
2) Ionize the vapor by passing an electric current through it. This electric current
strips away an electron, leaving a +1 cation (usually the cation is +1, but it
can occasionally be +2) in the gaseous phase.
3) Accelerate the cations by means of negatively charged objects, sometimes
rings.
4) Pass the cations (of various speeds) through a dual-disk mechanism that has
offset slits. This simple mechanism only lets ions of the same speed through.
5) Pass the cations through two oppositely charged plates. The heavier ions will
be deflected less than the lighter ions. The higher charged ions (like +2 or
+3) will be deflected even more, but most of the ions are +1.
6) Have some type of recorder measure the relative abundance of each isotope.
The chart will look something like:
Electrons and Atomic Structure
We will re-visit electrons and their role in the chemical and physical properties of
elements later on. Here, we give just a brief introduction to the electron and it’s
role in ion formation and flame tests.
Formation of Ions
A neutral atom has no net charge. The electrons and protons are in equal
numbers, so the + and – charges cancel out. An atom can form an ion, however,
when it gains or loses electrons. An atom that loses e- is called a cation and has
a positive charge. An atom that gains e- is called an anion, and has a negative
charge. The metals typically lose electrons to form cations and the nonmetals
usually gain electrons to form anions.
EX: A typical potassium ion (K+) has how many e-, no, and p+?
EX: A typical oxide ion (O2-) has how many e-, no, and p+?
The Bohr Model of the Atom and Flame Tests
In 1913 Niels Bohr proposed a model in which the electrons circled the nucleus,
like the planets orbit the sun. This model is sometimes called the planetary
model. This model also proposed a very insightful idea: that the electrons could
only occupy certain positions around the nucleus, and the farther out electrons
got, the greater the electron’s energy. An electron could only move to a higher
(or lower) energy level if it acquired (or lost) a certain amount of energy. This
idea explains the phenomena observed in flame tests
Mass Defect (not in book)
You may notice that some atoms seem particularly light. In the example above,
the mass of each isotope of neon is slightly less than you would predict. For
example, Neon-20, with 10 protons,10 neutrons and 10 electrons has a mass of
19.992 amu (you would expect it to have a mass of just over 20 amu). This slight
mass deficiency is due to the fact that some of the mass of the atom is converted
to energy (called nuclear binding energy) to hold the nucleus together. The
amount of mass lost can be used to calculate the nuclear binding energy by
using Einstein’s famous equation E = mc2.
EX:
A proton has a mass of 1.00728 amu, while a neutron has a mass of
1.00867 amu. The electron has a very small mass of 0.00055 amu.
Given this information, calculate the mass defect (the “missing mass”) of
an oxygen-18 atom, which has a mass of 17.99916 amu.
It is interesting to note that the element with the most mass (as a percentage)
converted to nuclear binding energy is the element iron. This fact implies that the
element iron has the most stable nucleus. As such, nuclear processes, such as
fission and fusion, will release energy when the process results in elements
closer to iron on the periodic table. This observation will be brought up again in
the next chapter, which focuses on nuclear chemistry.
Chapter 19 - Nuclear Chemistry
Introduction
In normal chemical reactions, the electrons play the critical role. Indeed, the
electrons are the part of the atom that determine the chemical properties of an
element. In ordinary chemical reactions, atoms are rearranged; they are not
changed into other elements. In nuclear reaction atoms can and do change from
one element to another. Obviously, this change requires a change in the nucleus
of the atoms involved. This chapter focuses on the changes that the nucleus
undergoes as atoms are changed into other elements.
Some General Principles
There are approximately 2000 different isotopes of elements. Of these, only 279
have a stable nucleus. All elements with atomic numbers greater than 82 will
undergo nuclear decay, although some will decay rather slowly. For some
reason, lighter elements are stable when the neutron/proton (n/p ratio) is close to
1. For the heavier elements, stable nuclei occur when the neutron/proton ratio is
close to 1.5. There is a “band of stability” for the different stable nuclei. By
undergoing nuclear decay, elements move toward the band of stability.
A few anecdotal comments are appropriate. First of all, for some strange reason,
isotopes with a number of protons or neutrons or sum of protons and neutrons
equal to 2, 8, 20, 28, 50, 82 or 126 have unusual stability. For instance, 42 He,
16
20
88
208
8 O, 10 Ne, 38 Sr, and 82 Pb meet these requirement, and show unusual stability.
Also, even numbers of protons and neutrons are preferred over odd numbers.
For instance, there are 157 stable isotopes with an even number of both protons
and neutrons. There are only 5 stable isotopes with an odd number of both
protons and neutrons.
Writing Nuclear Equations
An isotope (or nuclide, as it is called in nuclear chemistry) takes the form: ZA X,
where X is the element symbol, Z is the atomic number, and A is the mass
number. In a nuclear equation both the atomic number (Z) and the mass number
(A) must be the same on both sides of the equation. That is, the sum of the Z
values on both sides of the arrow must be equal, and the same restriction applies
to the A values. (This results from conservation of mass and conservation of
charge - you can kind of think of Z as representing the charge, and A
representing the mass). The following examples illustrate this point:
Write the other product in the following nuclear reactions:
(a)
239
94
Pu
(b)
238
92
U
(c)
42
19
K →
(d)
9
4
Be
(e)
201
80
→
+
+
4
2
+ _______
He → _____ +
4
2
0
1
1
1
He
(f) _______ +
n
e + _____
H
Hg +
1
0
→ _______ +
0
1
4
2
He
e → _____
1
0
n →
142
56
Ba
+
91
36
Kr + 3 01 n
Types of Radiation
When an isotope undergoes a nuclear decay, it moves toward the band of
stability. For heavy nuclei (those with 84 or more protons), a main type of
radioactive decay is alpha decay, which makes the nucleus lighter, and less
highly charged. For nuclei above the band of stability (those with a
neutron/proton ratio that is too high), beta emission will likely occur. Beta
emission lowers the n/p ratio. For nuclei below the band of stability (those with
too low a n/p ratio) positron emission or electron capture will increase the n/p
ratio. These results can be summarized as:
▪ Heavier atoms (Z > 83) undergo alpha emission to become lighter and to reduce
the number of protons in the nucleus
▪ Atoms with a neutron/proton ratio that is too high will undergo beta emission
▪ Atoms with a neutron/proton ratio that is too low will under positron emission
and/or electron capture
Alpha () Radiation
Alpha radiation consists of helium nuclei (2 protons and 2 neutrons) that have
been emitted from a radioactive source. They possess a +2 charge. In writing
nuclear reactions, an alpha particle is written as 42 He or as 42 . The charge is
omitted.
222
88
Ra →
4
2
He +
218
86
Rn
When an atom loses an alpha particle, the atomic number is lowered by two and
its mass number is lowered by four. Because of their large mass and charge,
alpha particles are blocked by clothes, skin, or a piece of paper. Heavier
elements become lighter by undergoing this type of nuclear decay.
EX:
Write the equation for Thorium-230 undergoing α emission. Would the
product of this decay be radioactive? Explain.
Beta () Radiation
Beta radiation consists of fast-moving electrons formed by the decomposition of
a neutron of an atom. The nuetron breaks into a proton and an electron, which is
ejected.
14
6
C →
14
7
N
+
0
1
e
( emission)
The mass number of the resulting atom remains the same, while the atomic
number has been increased by 1. The overall effect is to decrease the
neutron/proton ratio. Since beta particles are smaller and have less charge than
alpha particles, they are more penetrating. They can be stopped by aluminum
foil or wood. They will penetrate about 4 mm into exposed skin.
EX:
Write the equation for Thorium-234 undergoing β-emission. Calculate the
n/p ratio of the isotope before and after emission.
Gamma () Radiation
Gamma radiation is electromagnetic radiation, like X-rays or microwaves.
Gamma radiation is often emitted by the nuclei of disintegrating radioactive
atoms along with alpha or beta radiation. This type of radiation has no effect on
the neutron/proton ratio. Gamma radiation is like X-rays in that they are very
penetrating and have the potential to be very dangerous. Even several feet of
concrete or several inches of lead are only partially effective at blocking gamma
radiation.
222
88
Ra →
238
92
U →
4
2
4
2
He +
He +
234
90
218
86
Rn + 00 
Th + 2 00 
Decay Series
Often a radioactive nucleus will go through a series of radioactive decays before
stability is reached. For instance, U-238 goes through eight alpha decays and
six beta decays before reaching Pb-206. See page 271 for the decay series.
Positron Emission and Electron Capture
Two lesser-known forms of nuclear transformations are positron emission and
electron capture. Both of these processes increase the neutron/proton ratio. A
positron ( 01 e) is a particle with the same mass as the electron but opposite
charge. A positron is produced when a proton is changed to a neutron plus a
positron.
22
11
Na → 01 e +
22
10
Ne
Electron capture occurs when the nucleus captures an inner-orbital electron.
Gamma rays are always produced in electron capture. Unfortunately for the
alchemists out there, it happens too rarely to be a practical method of turning
mercury into gold!
201
80
Hg +
0
1
e →
201
79
Au +
0
0

EX: Write the equation for mercury-196 undergoing positron emission and
electron
capture. Calculate the n/p ratio before and after the decay.
positron emission:
electron capture:
EX:
Each of the following pairs contains one stable and one unstable isotope.
For each of the pairs, choose the unstable isotope, and state what type(s)
of radiation the unstable isotope would likely undergo.
6
Li or 8Li
8
B or 10B
195
Pt or 210Po
Detection of Radioactivity and the Concept of Half-life.
The most familiar instrument for measuring radioactivity levels is the Geiger
counter. High energy particles from radioactive decay produce ions when they
travel through matter. The probe of the Geiger counter contains argon gas which
is ionized by rapidly moving particles. The ion causes a quick pulse of current
which can be counted.
The half-life of a radioactive isotope is the time it takes for half the of the original
sample of nuclei to decay. For example if a certain radioactive sample contains
400 nuclei and the half –life is 15 minutes, then there will be 200 nuclei after 15
minutes, 100 nuclei after 30 minutes, 50 nuclei after 45 minutes, etc…. Some
radioactive elements have very long half-lives. For instance U-238 has a half-life
of 4.5 billion years. So any sample of U-238 that exists (or is produced) is likely
to be around for a long, long, time.
EX:
How long will it take for 40.0 grams of Pa-234 (half-life: 1.20 minutes) to
decay to only 1.25 grams? Express your answer both as a number of
half-lives and minutes.
EX: Consider the decay of 60 grams of a radioactive substance with a half-life of
6 minutes. Plot the mass of substance remaining as a function of time on
the graph below.
Radioactive Dating
This technique uses 14C to determine the approximate age of objects that were
made of once-living material. Carbon-14 is continuously produced in the
atmosphere when neutrons from space collide with Nitrogen-14.
14
7
N +
1
0
n →
14
6
C +
1
1
H
The 14C then decomposes by β-decay.
14
6
C →
14
7
N
+
0
1
e
The two processes of 14C production and 14C decay balance out, producing a
relatively constant amount of 14C in the atmosphere. This radioactive carbon
becomes part of the plant material in the region, which is often ingested by local
herbivores. When an organism dies, it stops taking in 14C, and only 14C decay
takes place in the decaying matter. Since the half life of carbon 14 is known to
be 5730 years, knowing the amount of carbon-14 will allow the approximate age
to be determined.
EX:
An ancient wooden spear only contains about 25% as much
radioactive carbon-14 as a modern piece of wood. About how old is the
spear?
Nuclear Transformations
It was first discovered by Rutherford in 1919 that elements could be converted
into other elements by bombardment with other particles. For instance, he was
able to convert N-14 to O-17 with bombardment by and alpha particle:
14
7
N +
4
2
He →
17
8
O + 11 H
However, because a positive alpha particle is repelled by the positive charge of
the target nucleus, they must be moving at a very high speed to penetrate the
target. It is easier for neutrons to penetrate. In 1940, neptunium was produced
by neutron bombardment of U-238. The process initially gives U-239, which
decays to Np-239 by β-decay.
238
92
U + 01 n →
239
92
U →
239
93
Np +
0
1
e
All elements of atomic number 93 and larger are known as the transuranium
elements, and were produced synthetically by bombardment of the nucleii of
lighter elements.
Nuclear Energy
The forces that hold together the protons and neutrons in the nuclei of atoms are
much larger than the forces that bind atoms together to form molecules. In fact,
the energies associated with nuclear processes are more than a million times
those associated with chemical reactions. This fact potentially makes the
nucleus a very attractive source of energy. Fusion involves the combining of light
nuclei to form heavier nuclei. Fission involves splitting a heavy nucleus into two
nuclei with smaller masses. The cut-off is iron: lighter elements can undergo
fusion to release energy, while heaving elements can undergo fission to release
energy.
Nuclear Fission
Nuclear fission was discovered about seventy years ago when U-235 atoms
were bombarded with neutrons, producing lighter elements (and three neutrons)
in the process:
235
92
U +
1
0
n →
141
56
Ba +
92
36
Kr + 3 01 n
The process released a tremendous amount of energy – about 26 million times
as much energy if an equivalent amount of ordinary methane fuel is burned! The
process can be self-sustaining (called a chain reaction) if at least one of the three
neutrons produced hits another U-235 atom. To accomplish this task, a certain
minimum mass (called the critical mass) of U-235 is needed. If the sample is too
small, too many neutrons escape before they have a chance to cause a fission
event, and the process stops.
Fusion
The process of combining two light nuclei is known as fusion. (The cut-off is iron:
elements heavier than iron will release energy when they undergo fission;
elements lighter than iron will release energy when they undergo fusion.) Again,
tremendous amounts of energy are produced. Our sun gives off vast amounts of
energy as hydrogen is fused into helium.
There are many efforts being conducted to try to find a way to harness the power
of fusion here on earth. The main problem comes from shooting one positively
charged nucleus at another – the like charges of the protons repel and make
fusion very difficult. In fact, it takes temperatures of about 40,000,000 K to get
two hydrogen atoms moving fast enough to facilitate fusion. There is talk of “cold
fusion” - getting fusion to occur at more manageable temperatures. However, the
future of “cold fusion” here on earth is unclear at this time.