Download 2.1 Imaging and Moving Individual Atoms

2. Atoms and Elements
2.1 Imaging and Moving Individual Atoms 43
2.2 Early Ideas about the Building Blocks of Matter 45
2.3 Modern Atomic Theory and the Laws That Led to It 45
2.4 The Discovery of the Electron 49
2.5 The Structure of the Atom 51 2.6 Subatomic Particles: Protons,
neutrons, and Electrons in Atoms 53
2.7 Finding Patterns: The Periodic Law and the Periodic Table 58
2.8 Atomic Mass: The Average Mass of an Element’s Atoms 64
2.9 Molar Mass: Counting Atoms by Weighing Them 66
Key Skills: Using the Law of Definite Proportions (2.3)
Chapter 2. Atoms and Elements.
Atoms were first considered as the smallest element of matter. What happens if
someone took something and cut it in half, then cut that in half and kept going? The original
concept of an atom follows from a presumed result of this thought experiment.
IBM scientists discovered how to move and position individual atoms on a metal surface using a
scanning tunneling microscope (STM). The technique was demonstrated in April 1990 at IBM's Almaden
Research Center in San Jose, California. Some of the microscopic techniques are described below.
2.1 Imaging and Moving Individual Atoms
Microscopy is the technical field of using microscopes to view samples and objects
that cannot be seen with the unaided eye (objects that are not within the resolution range of
the normal eye. Because of the limitations imposed by the visible light used in optical
microscopy surface image resolution cannot be lower than a m which is not atomic resolution
(nm). There are three well-known branches of microscopy: optical, electron, and scanning
probe microscopy.
1) Optical Microscopes or light microscopy uses visible light that transmitted through
or reflected from the sample using single or multiple lenses to allow a magnified view of the
sample.] The resulting image can be detected directly by the eye or captured on photographic
plate or digitally.
2) SPM-Scanning Probe Microscopy is a branch of microscopy that map the surface
features an images of using a probe a cantilever that scans the specimen. SPM works very
similar to a blind person using his cane to map the surface features of the road and obstacles.
There are two types SPM: a) a)STM-Scanning Tunneling Microscope, b) Atomic Force
Microscope
a)STM-Scanning Tunneling Microscope
b) Atomic Force Microscope
3) Electron beam Techniques
SEM-Scanning Electron Microscope
TEM-Transmission Electrum Microscope
2.1 Atomic Structure and Subatomic Particles Page.42
Radioactivity
2.1 Imaging and Moving Individual Atoms page 43
2.2 Early Ideas about the Building Blocks of Matter page 45
2.3 Modern Atomic Theory and the Laws That Led to It page 45
2.4 The Discovery of the Electron 49
2.5 The Structure of the Atom page 51
2.6 Subatomic Particles: Protons, Neutrons, and Electrons in Atoms page 53
2.7 Finding Patterns: The Periodic Law and the Periodic Table page 58
2.8 Atomic Mass: The Average Mass of an Element’s Atoms page 64
2.9 Molar Mass: Counting Atoms by Weighing Them page 66
Henry Becquerel had already noted that uranium emanations of ionizing
radiation could turn air into a conductor of electricity. Using sensitive instruments,
radiation counters, invented by Pierre Curie and his brother, Pierre and Marie Curie
measured the ability of emanations from various elements to induce conductivity.
On February 17, 1898, the Curies tested an ore of uranium, pitchblende, for its
ability to turn air into a conductor of electricity. The Curies found that the
pitchblende produced a current 300 times stronger than that produced by pure
uranium. They tested and recalibrated their instruments, and yet they still found
the same puzzling results. The Curies reasoned that a very active unknown
substance in addition to the uranium must exist within the pitchblende. In the title
of a paper describing this hypothesized element (which they named polonium after
Marie's native Poland), they introduced the new term: "radioactive." Radioactivity is
a term that use to explain the instability of certain nucleus of atoms and their
disintegration into stable nucleus while giving of a-(He nuclei), b-(fast moving
electrons), and g-(high energy electromagnetic radiation) radiation.
Cathode-rays
Thomson's cathode ray tube experiments: Discovery of ElectronsElectrons:
Electrons are sub-atomic particles with a mass of 9.11 x 10-28g ( 1/1833
times mass of a proton) and a negative charge of 1.60 x 10-19 c (c=coulombs) or 1.60 x 10-19 c. Electron was first discovered by J.J. Thompson using cathode-ray
tubes or Crook's tubes. According to modern atomic theory an electron travels
around a nucleus made up of protons and
neutrons.
An electrical current is a stream of electrons
passing through a metal or a conductor. J.J.
Thomson used results from cathode ray tube
(commonly abbreviated CRT) experiments to
discover the electron. Thomson and a cathode
ray tube from around 1897, the year he announced the discovery of the electron.
Only the end of the CRT can be seen to the right-hand side of the picture. The two
plates about midway in the CRT were connected to a powerful electric battery
thereby creating a strong electrical field through which the cathode rays passed.
Thomson also could use magnets, which were placed on either side of the straight
portion of the tube just to the right of the electrical plates. This allowed him to use
either electrical or magnetic or a combination of both to cause the cathode ray to
bend. The amount the cathode ray bent from the straight line using either the
electric field or the magnetic field allowed Thomson to calculate the e/m ratio. e/m
ratio stands for charge-to-mass ratio of the electron.
Millikan's oil drop experiments: Measuring Electronic Charge
American physicist Robert Andrews Millikan (1868-1953)
designed
an
experiment to measure the electronic charge. Drops of oil were carried past a
uniform electric field between charged plates. After charging the drop with x-rays,
he adjusted the electric field between the plates so that the oil drop was exactly
balanced against the force of gravity. Then the charge on the drop would be known.
Millikan did this repeatedly and found that all the charges he measured came in
integer multiples only of a certain smallest value, which is the charge on the
electron, a negative charge of 1.60 x 10-19 c (c=coulombs) or -1.60 x 10-19 c.
Rutherford’s - particles scattering experiment: Nuclear atom
A New Zealander, Rutherford fired Alpha particles at an extremely thin gold foil. He
expected them to go straight through with perhaps a minor deflection. Most did go
straight through, but to his surprise some particles bounced directly off the gold
sheet! This means there something in the atom that deflected the alpha particles.
Rutherford hypothesized that the positive alpha particles had hit a concentrated
mass of positive particles, which he termed the nucleus.
2.2 The Nuclear Atom Page.45
Nucleus: The mass and the positive (+) charge of an atom are concentrated in the
center. This center is called nucleus, and it has radius of about 10-13 cm. Nucleus
contains protons and neutrons which are equal in mass. Number of protons in a
nucleus is called the atomic number (Z)
Proton
Proton is a sub-atomic and sub-nuclear particle. A proton has a mass of 1.67 x 10-24
g (which is 1833 times heavier than an electrons) and carries a positive charge of
1.60 x 10-19 c which is equal to the negative charge found on an electron . Protons
gives a positive charge to the nucleus of an atom. In a neutral atom, number of
electrons and protons are equal . Number of protons in a nucleus is called atomic
number (Z)
Discover of Atomic number and protons: Henry Moseley's X-ray experiment
The metal in the anode of the cathode-ray tube gives off x-ray when the when the
cathode rays hit the anode. Moseley measured the frequency of X-rays given off
and found that about half-the-mass of the atoms making the anode is directly
proportional to the square-root of the frequency. Moseley showed that the energies
were given in good approximation by:
EK = 3/4 (Z - b)2 EI,
in which Z is the atomic number of the element, b is an empirical screening
constant roughly equal to , and EI is the ionization energy of the hydrogen atom,
13.6 eV. This number (Z) he called atomic number later found to be the number of
protons in the nucleus.
Atomic number (Z): Number of protons in a nucleus of an atom is called atomic
number (Z), Z is characteristic to an element. An oxygen atom always have eight
protons and atomic number equal to eight. However, It is possible for an element to
have atoms with different masses by having different number of neutrons in the
nucleus. Atoms of an element having different number of neutrons in the nucleus
are called isotopes.
Discovery of Neutrons: Chadwick's bombardment of 9Be with -particles:
There must be uncharged particles in the nucleus to account for the missing mass
of atoms after considering number of electrons and protons. Chadwick observed a
particle in the nucleus of the same mass as a proton( 9Be + 4He --> 12C + 1n), but
without a charge in a nuclear reaction of 9Be with "-particles. His experiment led to
the discovery of neutron. Neutrons are sub-atomic and sub-nuclear particles. A
neutron has a mass of 1.67 x 10-24 g which is equal to that of a proton, but it is
neutral. Neutrons along with protons contribute to the mass or bulk of the matter
or atoms.
Structure of Atom
Atom is the fundamental unit of matter. An atom has a nucleus and electrons. The
electrons are presumed to be rotating around the nucleus in orbits similar to
planets in the solar system. Nucleus contains protons and neutrons, which have
equal mass. Volume or the radius of an atom is, determined by the outermost orbit
of electrons, in the range of 10-8 cm. Number of protons in the nucleus is called
atomic number (Z), which characterizes the type of element. It's possible for
atoms of an element to have different masses (i.e. different # of neutrons). They
are called isotopes.
2.2The Sizes of Atoms and the Units Used to Represent Them Page.46
The Size of Atoms and Units Used to represent them: Mass and charges of
electron, proton and neutron
Atoms are made of small particles called protons, neutrons, and electrons. Each of
these particles is described in terms of measurable properties, including mass and
charge. Mass is the amount of matter that an object contains. The proton and
neutron have roughly the same mass and have approximately one thousand times
the mass of the electron. The proton and electron have equal, but opposite,
electrical charges. A neutron does not have an electrical charge.
Particle
Proton
Neutron zero
Electron
Charge Mass (g)
+1.60 x 10-19 C
0
-1.60 x 10-19 C
Mass
1.672 x10-24 g
1.675 x 10-24g
9.109 x 10-28g
(amu)
1.0073
1.0087
5.5 x 10-4
It is very hard for anyone to really understand how small something like the atom
or its nucleus really is. The only good way to visualize it is to make a comparison to
the relative sizes of things we see in our daily life.
If an atom were the size of the period at the end of a sentence or a pixel on your
screen, a person would be 1000 miles tall! That is how small the atom is. Nucleus
has a radius of about 10-13 cm. An atom has a radius of about 10-8 cm or
angstroms.
If an atom were the size of a football stadium, with the electrons out around the
upper deck, the nucleus down at midfield would be smaller than the coin flipped at
the start of the game. An atom is roughly about 0.2 nm across (nm means nano
meter, where nano is the metric prefix meaning 10-9) although the electrons spend
most of their time in a region about 0.1 nm = 0.0000000001 meters in diameter.
Atoms, Molecules and Ions.
Atom - The smallest unit of an element made up of nucleus and electrons that has
all of the properties of an element.
Molecule -The smallest unit of a pure substance that has the properties of that
substance. It may contain more that one atom and more than one element.
Ions - Charged particles formed by the loss or gain of electrons from between
atoms or molecules.
Na (sodium atom )
-- Na+ ( sodium ion) + e- (electron) Positive Na+
is also called a cation.
Cl (chlorine atom ) + e- (electron) -- Cl- ( chloride ion) Negative ClNa+ is also called anion.
a single
atom
(of an
element)
A homonuclear
diatomic molecule
(of an element)
a heteronuclear diatomic
molecule
(of a compound)
Note: Atoms don't have a color. The colors here are used to differentiate
between kinds of atoms.
2.4 Uncertainty and Significant Figures Page.52
Measurement Systems
Measuring system is an integral part of any commerce or science to
agree on the quantities of in their business and practices. In England a
measuring system for the trading volumes was not properly standardized
until the 13th century. For example, until gallon was made the standardized
measure of volume consolidating different types of gallons (ale, wine and
corn).
In France and in 1799, a decimal system called metric system using
centimeter, gram, and second (CGS system) for length, mass and time,
respectively. All units are compared to a standard measure: meter was
defined as being one ten-millionth part of a quarter of the earth's
circumference and 100 centimeters equals a meter.
Prefixes used in abbreviating measurements
Prefixes allows simplifying the numbers with many zeros before and after
the decimal place.
Convert measurements to a unit that replaces the power of ten by a
prefix:
6.80 x 10-9 m (6.08 nm) 7.14 x 10-6 s (7.14 m) 2.88 x 10-3 g (2.88 mg)
2.54 x 10-2 m (2.54 cm) 4.56 x 103 g (6.08 kg) 7.14 x 106 s (7.14 Ms)
Metric System Units-SI system
Later a comprehensive Le Systeme international d'Unites (SI unit
system) was created in 1960 and has been officially adopted by nearly all
countries. SI units are based prefixes and upon 7 principal units, 1 in each of
7 different categories measurements.
Category
Name
Abbrev.
Length
Mass
Time
Electric current
Temperature
metre
kilogram
second
ampere
kelvin
m
kg
s
A
K
Amount of
Luminous intensity
mole
candela
Mol
cd
2.3 Exact and Inexact Numbers
Exact Measurements For certain types of number associated with conversion
factors are considered “exact.” For example, there are exactly 16 ounces in one
pound. The number 16 would have as many decimal places or significant figures as
needed. So one pound has 16.000000000000.... Ounces. If you see any numbers
you use in a calculation comes from a definition you could assume they are exact
numbers.
Exact Measurements In most of measurements the number associated with them
are considered “inexact.”
For example, if you measure the mass of a certain
object on a balance and found that it has a mass of 25.0125 g, 25.013, 25.01 g
25.0 g or 25 g with a decimal place rounded off to a place at right depending on the
decreasing accuracy of the balances used. If you use a number in a calculation
which comes from a experimental measurement you could assume they are inexact
numbers.
Which types of numbers are considered “exact?” Below are the general
rules. Metric to metric system conversion factors are exact
1. e.g. 1 m = 100 cm or 1 m/100 cm (In this conversion, 1 and 100 are
both exact.)
Conversions between English and Metric system are generally NOT
exact. Exceptions will be pointed out to you.
2. e.g. 1 in = 2.54 cm exactly (1 and 2.54 are both exact.)
3. e.g. 454 g = 1 lb or 454 g/1 lb (454 has 3 sig. fig., but 1 is exact.)
An example of an extensive property is
a. freezing point. b. color. c. length. d. density.
a
b
c
d
e
Clear
Uncertainty in Measurement and Significant Figures
An inexact numbers always comes out of an experimental measurement.
They have been rounded off to show the uncertainty in the measurement. For
example, if you measure the mass of a certain object on a balance and found that it
gives a mass of 25.0125 g, 25.013, 25.01 g 25.0 g or 25 g with a decimal place
rounded off to a place at right depending on the decreasing accuracy of the
balances used. A measurement is always written down after considering the
instrumental uncertainties. The uncertainly of a measurement could be conveniently
expressed as a significant figure (SF). The right most digit in 25.0125 g which
is 5 at the 4th decimal place is considered uncertain digit. Describe uncertainty
and significant figures and how they are obtained for a measurement. The
significant figure for this inexact number is obtained counting the other digits to the
left from the uncertain digit. Therefore, 25.0125 g would have 6 significant figures:
25.013 (5 SF) , 25.01 g (4 SF) 25.0 (3 SF) g and 25 g( 2 SF). Lower the SF,
higher the uncertainty of the number and less accurate.
GENERAL RULES FOR FIGURING WHICH NUMBERS are significant.
1. ZEROS used to "place" the decimal are NOT significant figures: 0.015 g = 2
SF
2. LEADING ZEROS BEFORE all the digits are NOT significant: 000340 = 3
SF and 0.000216 g = 3 SF
3. TRAILING ZEROS after all the digits are SIGNIFICANT:1.500 g= 4 SF
4. SANDWICH ZERO WITHIN a number are SIGNIFICANT: 0.0105 g = 3 SF
and 10.5 g = 3 SF
0.027 g = 2 SF (LEADING zeros BEFORE all the digits are NOT significant)
2.600 m = 4 SF (TRAILING zeros after all the digits are SIGNIFICANT)
210.05 s = 5 SF (SANDWICH zeros WITHIN a number are SIGNIFICANT)
0.0306 Kcal = 3 SF (LEADING zeros BEFORE as well as SANDWICH zeros
WITHIN are SIGNIFICANT)
How many significant figures are in the following numbers:
a) 0.0945 (3 SF) b) 83.22 (4 SF)
c) 106 (3 SF) d) 0.000130 (3 SF)
Deduce the number of significant figures contained in the following:
a) 16.0 cm (3 SF) b) 0.0063 m (2 SF) c) 100 km (3 SF)
d) 2.9374 g (5 SF) e) 1.07 lb/in2 (3SF)
How many significant figures are in the following measurements?
a) 25.9000g (6 SF) b) 102 cm (3 SF) c) 0.002 m (1 SF) d) 2001 kg (5 SF)
0.0605 s (3 SF) f) 21.2 m (3 SF) g) 0.023 kg (2 SF) h) 46.94 cm (4 SF)
453.59 g (5 SF)
j) 1.6030 km (5 SF)
e)
i)
Uncertainty, Error, Accuracy, and Precision of measurements
Uncertainty is expressed in terms of the rounding off to a significant figure.
e.g. 25.013 ( 5 SF) , 25.01 g ( 4 SF) 25.0 (3 SF) g and 25 g( 2 SF). Note that
greater the number of significant figures, the greater the precision.
Precision versus Accuracy:
Precision = How close measurements agree: If you take more reading of the same
measurement how close they are.
e.g. 25.0125 g, 25.0124 g and 25.0126 g are more precise than 25.0225 g,
25.10127 g and 25.0326.
Accuracy = how close measurement is to the true value: something could be
precise but inaccurate if the value is off by calibration error.
e.g. Measurements 25.0125 g, 25.0124 g and 25.0126 and the true value 25.0125
g are both precise and accurate.
e.g. Measurements 25.0125 g, 25.0124 g and 25.0126 and the true value 25.0125
g are both precise and accurate.
e.g. 25.0225 g, 25.10127 g and 25.0326 g and the true value 26.0125 g are
neither precise nor accurate.
Significant Figures and Mathematical Operations
Most of the experiments involve calculation of a answer (derived quantity)
from basic measurements with various units to a complex quantity with derived
units. A simple example would be calculation of velocity of an object (car) travelling
certain distance 356.5 miles in a given time in 4.8 hours. Question is how we obtain
a velocity with correct uncertainties (SF) corresponding to uncertainties of distance
and the time. Some of derived quantities involve additions/subtractions and/or
multiplication/division.
General rules for significant figure in addition/subtraction:
254 mL
- 54.1 mL
208.1 mL (4 SF)
208 mL (3 SF)
125.4
g
2.54 g
======
127.94 g
127.9 g (4 SF)
Rounding Off Numbers
1. "extra" digit is LESS than 5-drop it.
2. "extra" digit is MORE than 5-ADD
1.
3. "extra" digit is 5 “Odd rule“
e.g. 2.535 is rounded as “2.54
4. "extra" digit is 5 “Even rule“
e.g. 2.525 is rounded as “2.52”
1. When adding or subtracting numbers, all numbers must have the same units.
2. The answer can have no more decimals than the measurement with the fewest
DECIMALS.
Significant figures in multiplication/division calculations
1. When multiplications or divisions of numbers, all numbers must have the same
units.
2. The answer can have no more significant figures than the measurement with the
fewest SIGNIFICANT FIGURES.
(231.54 * 43)/433.4 = 22.972358 (231.54 (5 SF) 43(2 SF) 433.4 (4 SF)
= 22.972358 = 21 (2 SF)
= 21 (2 SF)
Calculate 3.21 cm x 15.091 cm =18.301 cm = Ans. 18.3 cm (3 SF)
Calculate 3.82 x 1.1 x 2.003 = 8.416606 = Ans. 8.4 (2 SF)
Calculate 13.87 ÷ 1.23 = 11.27642276 = Ans. 11.3 (3 SF)
Calculate 0.095 ÷ 1.427 = 0.066573231 = Ans. 0.067 (2 SF)
In a long calculation involving mixed operations, carry as many digits as possible through
the entire set of calculations and then round the final result appropriately. For example,
(5.00 / 1.235) + 3.000 + (6.35 / 4.0)
=4.04858... + 3.000 + 1.5875=8.630829... 5=8.6
Scientific Notation
Scientific notation uses power-of-10 to express an extremely large or small
numbers. Scientific notation has a regular number with correct significant figure
with a value between 1 to 10, and a power of 10 by which the regular number is
multiplied. E.g. 0.067 is converted to scientific notation: 6.7 x 10-2
The table shows several examples of numbers written in standard decimal notation
(left-hand column) and in scientific notation (right-hand column).
Number in decimal form with
significant digits color
Scientific notation with correct
significant digits
1,222,000.00
1.222 x 10
6
34,500.00
3.450 x 10
4
0.00003450000
3.45 x 10
-0.0000000165
-1.65 x 10
-5
-8
Scientific notation makes it easy to multiply and divide gigantic and/or minuscule
numbers. To obtain the product of these two numbers (the coefficients) are
multiplied, and the powers of 10 are added. This produces the following result.
2.56 x 1067 x -8.333 x 10-54 = (2.56 x -8.333)(1067 x-54) =
(-21.33248)(1013) = (-21.3)( 1013)
= (-2.13)(1014) = -2.13 x 1014
Now consider the quotient of the two numbers multiplied in the previous
example:
(3.46 x 10
57
) / (9.431 x 10
-75
)
To obtain the quotient, the coefficients are divided, and the powers of 10 are
subtracted. This gives the following:
= ((3.46 / (9.431)) x (10 57/10-75)) = ((3.46 / (9.431)) x (10
= (3.46 /9.431)) x 10 57+75 = (3.46 /9.431)) x 10 57+75
= 0.366875199 x 10137 = (3.66875199 x 101 ) x 10137
= (3.67) x ( (101 ) x 10137) = (3.67 x (10138) = 3.67 x 10138
57
x10-(-75))
Conversion Factors and Dimensional Analysis
Conversion Factors are used to convert a measurement to another with different
units. They are used for the length, mass, area, volume, temperature, energy,
force and time conversions as listed below:
Conversion Factors
Length
Mass
Area
1 ft =12 in
1 yd = 3 ft
1 mi 5280 ft =
1mi = 1.609km
1 in =2.54 cm
1 m =3.281 ft
1 lb = 16 oz
1 ton = 2000 lbs
1 lb = 453.59 g
1
1
1
1
Energy
1 cal = 4.18681 J
Btu=1.05506E3 J
1 food cal = 1 kcal
Pressure
1 atm = 760 torr
1 atm = 1.01325E5 Pa
1 mmHg = 1 torr
1 mmHg = 1.333E2 Pa
1 Psi = 6.89476E3 Pa
Volume
acre =4.048x103 m2
acre =4840 yd2
mile2=2.589x106 m2
mile2= 640 acres
Time
60 min = 1 hr
24 hr = 1 day
365.25 days = 1 year
1
1
1
1
gal = 4 qt
qt = 2 pt
gal = 3.785 L
L = 103 mL
1 mL = 1 cm3
Temperature
? K = (x) °C -273.15)
? °C = (x) K + 273.15
? °C = (5/9) ((x)°F -32)
? °F = (9/5)(x)°C +32
Simple unit conversations using factor label method
Length
How many meters are in a 4 cm?
Conversion factor: 1 cm = 10-2 m or
1 cm
1 cm = 10-2 m or
10-2 m
4 cm
10-2 m
1 cm
Align the conversion factor to a cancel cm
= 4 x 10-2 m
How many inches are in 1 meter? Given the conversion factors 1 inch = 2.54 cm
and 1 meter = 100 cm
1.00
m
100 cm
1m
1 in
2.54 cm
= 39.37008 m
= 39.3 m
or
1.00
m
x
100 cm
1m
x
1 in
2.54 cm
= 39.37008 m
Note digits in blue are exact and was not considered for SF
= 39.3 m
Convert
2.4 meters to centimeters (240 cm or 2.4 x 102 cm)
Mass
How many grams (g) in 150 pounds (lb) given the equalities 1 lb = 0.454 kg and 1
kg = 1000 g?
150 lb
0.454 kg
1 lb
1000 g
1 kg
= 68100 g
= 6.81x 104 g
Scientific notation allows to show SF clearly.
Convert 65.5 centigrams to milligrams 655 mg)
Convert 5 liters to cubic decimeters (5 dm3)
1. The density of a substance is 2.7 g/cm3. What is the density of the substance
in kilograms per liter? 2.7 kg/L
2. A car is traveling 65 miles per hour. How many feet does the car travel in
one second? 95 ft/sec
3. The density of water is one gram per cubic centimeter. What is the density
of water in pounds per liter? 0.45 lb/L
4. How many basketballs can be carried by 8 buses? 1 bus = 12 cars, 3 cars
= 1 truck, 1000 basketballs = 1 truck 32 000 basketball
Area unit: m2 is the base unit of area
(1)2 cm2 = (10-2)2 m2
1 cm2 = 10-4 m2
Volume unit: m3 is the base unit of volume.
1 cm = 10-2 m
cube each number and unit in the conversion factor
(1)3 cm3 = (10-2)3 m3
1 cm3 = 10-6 m3
2.5 Atomic Numbers and Mass Numbers Page.54
Isotopes and Isotopic symbols & Mass
Isotope: Atoms of the same element with different masses or different number of
neutrons in the nucleus. E.g. 1H (hydrogen is with one proton and one electron) and
2
H (deuterium with one proton, one neutron and one electron).
Isotopic symbol: Element symbol (X) indicating number of protons or atomic
number (Z) written as left subscript, and mass number (A), total of number of
protons and neutrons written as left superscript.
Mass Numbers (A): Number of neutrons and protons together in a nucleus of an
atom is called mass number (A), An element could have different atoms with
different A values. Therefore It is possible for an element to have atoms with
different masses by having different number of neutrons in the nucleus. Atoms of
an element having different number of neutrons in the nucleus are called isotopes.
A
X
Z
12
E.g carbon-12:
6
C
or simply written as 12C because once atomic symbol is known atomic number is
known
from
the
periodic
table.
12
The scale on the detector plate of mass spectrometer is calibrated using C isotope
and
gives
mass
of
each
isotope.
Atomic mass unit (amu) or amu scale is defined as the one-twelfth (1/12) mass
of
12C
isotope.
12
1 amu = (1/12) mass of
C isotope
The position of the peaks in the mss spectrum thus directly gives its mass in
amu, and their relative compositions (abundance) can be directly obtained from
the intensity of each peak.
Mass spectrometer provides mass of isotopes of elements and their natural
abundance or relative composition of an element.
For example, hydrogen is a mixture of 1H (hydrogen) and 2H (deuterium) in the
ratio 99.985% and 0.015%, respectively. Hydrogen also has a third artificial isotope
or radioactive isotope, Tritium-3H, which does not normally appear in the mass
spectrum since it has already decayed or converted to other two isotopes in
naturally occurring hydrogen.
2.6 isotopes and Atomic Weight Page.58
Mass spectrometer
Mass spectrometer is the instrument used to measure the masses of different
isotopes of elements. It is essentially an atomic balance. Atoms of an element are
made up of different isotopes ( i.e. atoms having different masses because of
different numbers of neutrons in their nuclei When a sample of an element is
injected into a mass spectrometer, it is vaporized into atoms and then to positive
ions by knocking off electrons. These ions are made to accelerate through
negatively charged plates (Mass spectrometer, page 54). Thus a fast moving ion
beam is obtained by having these ions passes through small slits in these plates.
This beam is then made to travel through a strong magnetic field which deflects
them onto a detector plate. Each line on the detector plate corresponds to an
isotope and the intensity of the line is proportional to relative composition or the
natural abundance of the particular isotope.
Average atomic weights: Average atomic weight is calculated based on the
masses of isotopes and their relative composition.
Most of the elements have two or more isotopes. The atomic weight reported
on the periodic table are average weights based on the masses of isotopes and
their relative composition. The equation for calculating average atomic mass (AAM)
for an element with two isotopes is:
M ax a + M b x b
----------------= AAM
100
Ma
= mass of isotope a
Mb
= mass of isotope b
a
= relative percent composition of a
b
= relative percent composition of b
AAM = Average atomic mass (Reported on the Periodic Table)
This equation applies to an element with two isotopes. Extra isotopes, Mc and c1 ,
Md and d , etc, could be added to the numerator of equation for elements having
more than 2 isotopes. Isotopic masses and relative composition are obtained from a
mass spectrometer.
Click here to do tutorials on atomic weights and isotopic abundance. Use back
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Sample Calculation
Gallium in nature consists of two isotopes, gallium-69, with a mass of 69.926 u and
a fractional abundance of 0.601; and gallium-71, with a mass of 70.925 u and a
fractional abundance of 0.399. Calculate the weighted average atomic mass of
gallium.
In this problem isotopic masses of 69Ga and 71Ga isotopes and their fractional
abundance are given. The average atomic mass or weighted average atomic
mass of Ga can be calculated using the equation after converting fractional
abundance to percent abundance or composition .
A.A.M =
Ma x a + M b x b
----------100
Ma (69Ga ) =68.926 u,
a = percent abundance of 69Ga = 0.601 x 100
Mb (71Ga ) = 70.925 u,
b = percent abundance of 71Ga = 0.339 x 100
We can obtain an equation with one unknown, AAM.
AAM) = 68.926x(0.601 x 100)+70.925 x(0.339x100)
100
AAM (Ga) = 4142.5 + 2829.9
100
AAM (Ga) = 6972.3 = 69.723
100
AAM (Ga) = 69.723 u (amu)
Weighted average atomic mass of gallium = 69.723
2.7 Amounts of Substances: The Mole Page.61
Why we need to use the concept of "mole" of atoms ( 6.022 x 1023
particles) in chemical stoichiometry?
Chemical equations are written in terms of atoms and molecules. However, we
cannot pick atoms individually and do reactions. Chemists always use mass in
grams as the amount in the reaction. Therefore, we need a conversion factor to
convert atoms and molecules to grams. Mole is the connection or the conversion
factor between atoms and grams.
Avogadro's Number
The name "Avogadro's Number" is just an honorary name attached to the calculated
value of the number of atoms, molecules, etc. in a gram mole of any chemical substance. Of
course if we used some other mass unit for the mole such as "pound mole", the "number"
would be different than 6.022 x 1023.
Atoms and molecules are weighed in the mass spectrometer in amu (atomic mass
units) not in grams. However, if you take atomic mass in grams the number of atoms is simply
6.022 x 1023 atoms or particles. In other words gram atomic weight or gram molecular weight
contains 6.022 x 1023 atoms, molecules or particles. This number is called Avogadro's number
or mole of particles. (Simply the mole). Mole is a convenient number to convert grams into
number of atoms or vice versa. Mole is also called the Chemist's dozen since it bring atomic
particle to a size that could handle easily similar to dozen of eggs. 1 mol = M.W. (molecular
weight) taken in grams 1 mol = 6.022 x 1023 particles 1 mol = 6.022 x 1023 atoms 1 mol = 6.022
x 1023 molecules 1 mol = 6.022 x 1023 ions
Define the most important conversion factors used in chemical stiochiometry. 6.022 x 1023
atoms = gram atomic weight
6.022 x 1023 molecules = gram molecular weight
6.022 x 1023 atoms C = 12.01 grams of carbon (C)
6.022 x 1023 molecules H2O = 18.02 g of H2O (water)
6.022 x 1023 = 1 mol 1 g = 6.022 x 1023 amu
1 amu = 1 g/mol
An atom weighs 7.47 x 10-23 g. What is the name of the element this atom belongs
to?
First convert g to amu and look up in the periodic table and find out the element. Conversion
factor: 1g = 6.022 x 1023 amu
6.022 x 1023 amu
7.47 x 10-23 g x
1g
=
44.98
amu
In the periodic table atomic masses increase generally with atomic number. Element with an
atomic mass closer to the value calculated is Sc (Scandium).
The element is Sc.
How many moles of iron (Fe) are present in 180.1g of elemental iron?
a.w. Fe = 55.85 g/mol This is a problem to convert grams to moles. Conversion factor
is 55.85 g Fe = 1 mol
180.1 g
Fe
x
1 mol
55.85 g Fe
= 3.225 mol Fe
What is the mass of 7.5 x 105 atoms of Cu in grams?
This problem requires conversion of atoms to grams. If you remember correctly this is
the definition of the mole. 1 mol = 63.55g Cu = gram atomic weight 1 mol = 6.022 x
1023 atoms 6.022 x 1023 Cu atoms = 63.55 grams Cu Therefore,
7.5 x 105 atom atoms63.55g
Cu
Cu
6.022 x 1023
atoms Cu
=7.9 x 1017
g Cu
 Describe the procedure to obtain molecular /formula weight from chemical formula.
 Describe the need of a "mole" to do a chemical reaction.
2.8 Molar Mass and Problem Solving Page.62
 Calculate number of moles given atomic masses and the chemical formula
2.9 The Periodic Table Page.64
 Describe Mendeleev short periodic table and how it relates to modern periodic table.
 Describe the use of periodic table: periods, groups, families, metals, non-metals, metalloids,
transition metals, actinides, lanthanides.
PORTRAIT OF A SCIENTIST: Ernest Rutherford Page.46
 What did he discover?
TOOLS OF CHEMISTRY: Scanning Tunneling Microscopy Page.48
 How does it work and what it can see?
TOOLS OF CHEMISTRY: Mass Spectrometer Page.56
 How does it work and what it measures?
ESTIMATION: The Size of Avogadro's number Page.62
 How big is this number?
PORTRAIT OF A SCIENTIST: Dmitri Mendeleev Page.64

How does it work and what it can see?
CHEMISTRY IN THE NEWS: Running Out of an Element? Page.69
 Can we find more and more elements?
CHEMISTRY YOU CAN DO: Preparing a Pure Sample of an Element Page.70

How you prepare pure sample of oxygen?