The Atomic Number, Mass Number, Isotopes and Relative Atomic Mass

                                The Atomic Number (Z) refers to the number of protons of an element in its nucleus. All atoms of an element have the same atomic number and no two elements can have the same atomic number. For example, the atomic number of calcium in the periodic table is 20, thus, the nucleus of calcium contains 20 protons. The Mass Number (A) refers to the mass of the nucleus or sum of the number of protons and neutrons in the nucleus. For example, calcium has 20 protons and 20 neutrons in its nucleus, therefore, the mass number of calcium is 40.

                                The Atomic Number and Mass Number of an element can written with its Atomic symbol.

In determining the number of subatomic particles in an atom, the following rules should be followed:

1.       The atomic number is equal to the number of protons (Z = p⁺)

2.       The mass number is the sum of the number of protons and neutrons in the nucleus.

(A = p⁺ + n⁰      or     A = Z + n⁰)

3.       The number of neutrons is equal to the mass number minus the number of protons.

(n⁰ = A - p⁺       or    n⁰ = A – Z)

4.       In a neutral atom, the number of protons and electrons are the same

If the atom is charged, subtract the charge to the number of protons (or Z).

Isotopes and Relative Atomic Mass

                                As technology progressed, scientists were able to discover that there are atoms of the same element with different mass numbers. They call these atoms as isotopes. These isotopes are atoms of the same element or atomic number but with different number of neutrons. For example, hydrogen has three isotopes, namely:

                              These isotopes of hydrogen have the same number of protons (atomic number) but have different mass numbers due to their difference in the number of neutrons. These isotopes have varying abundance. These percent abundance and mass numbers of isotope are used to get the relative atomic mass of the element. The Relative Atomic Mass of an element is the average atomic mass of all the naturally occurring isotopes of an element. The formula for the Relative Atomic Mass (A_R) is

THE FUNDAMENTAL PARTICLES OF THE ATOM

Electron (e^-)

John Dalton believed that the atom was the smallest component of matter. Little did he know that all would change as experiments on electricity were conducted. If you rub a balloon on your hair, small pieces of paper get attracted to it. What makes the pieces of paper stick to the balloon? John Dalton’s Atomic Theory was not able to explain this phenomenon. There must be something inside the atoms of the balloon that attracts the atoms of the pieces of paper.

Joseph John Thomson

This question was answered by Joseph John Thomson when he discovered the electrons, the negatively charged particle of an atom. Thomson discovered the electrons when he conducted experiments using a Crookes Tube, named after its inventor William Crookes, which was later called Cathode Ray Tube (CRT).

This CRT is a vacuum tube that produces a beam of light as residual air inside the tube gets ionized. This beams of light moves from cathode to anode. Thomson noticed  that the beam of light was attracted to a positive plate in electric field. Since the rule in electromagnetism is “like charges repel each other; unlike charges attract each other”, Thomson concluded from his experiment that the beam of light is negatively charged, and since matter also behave in the same manner as the beam of light, he also concluded that matter is made up atoms with negatively charged particles called electrons, a term introduced for this charge by George Johnstone Stoney. After discovering electrons, Thomson proposed a new atomic model which was called the Raisin Bread Model or the Plum Pudding Model of the Atom, where the raisins or plums are the corpuscles or electrons embedded on a sphere of uniform electrification.

The beam of light gets attracted
to a positive plate in electric field

Crooke's Tube

Raisin Bread or
Plum Pudding Model

Another scientist was awarded a Nobel Laureate in Physics for his measurement of the charge of the electron. It was Robert Andrews Millikan, an American experimental physicist. He was able to measure the charge of an electron by observing the movement of tiny droplets of oil in an apparatus with electrically charged plates and an x-ray source. Based on his experiment, the charge of an electron is -1.602 x 10^-19C (coulomb). Further calculations were made and the mass of an electron was found out to be 9.109 x 10^-31 kg.

Studies on Radioactivity

Radioactivity is another field of science that provided insights on the structure of the atom. Scientists like Henri Becquerel and Marie Curie noticed that some elements change in chemical properties as they emit radiation. Some of the known types of radiation during those times are the alpha, beta and gamma radiation.

Nucleus

A New Zealand-born British chemist and physicist named Ernest Rutherford conducted experiments using a newly discovered radiation called alpha particles to determine the composition of the atom. His experiment was called the Alpha Scattering Experiment, sometimes called as the Gold Foil Experiment.

Ernest Rutherford

Alpha-Scattering Experiment

Gold Foil as Alpha particles pass through

               In his experiment, a thin gold foil surrounded by a phosphor-coated detector was bombarded with positively charges alpha particles. In his experiment, he observed that most of the alpha particles just went through the gold foil, but to his surprise, some of the particles got deflected while some even bounced back. He concluded from his experiment that the atom is mostly empty space since most of the alpha particles just went through the gold foil. For the deflected alpha particles, he said that it must have hit something inside the atom that is of very small volume and is positively charged, which he called the nucleus. The nucleus covers the total mass of an atom.

                    From his discovery of the positively charged nucleus of the atom, he proposed a new atomic model called Nuclear Model of the Atom (sometimes called the Planetary Model), where the negatively charged electrons move around the positively charged nucleus of the atom, like the planets moving around the sun.

Nuclear Model of the Atom

Proton (p+)

Eugen Goldstein is sometimes credited for the discovery of the proton, the positively charged particle of the atom with a mass of 1.6726×10⁻²⁷ kg and a charge of +1. He conducted experiments using the Crookes Tube. He observed that as negatively charged electrons move from cathode to anode, there were also particles moving from anode to cathode, called the canal rays or anode rays. However, Goldstein was not able to single out the proton from the gases he worked with, leaving his search unfinished.

After his discovery of the nucleus, Ernest Rutherford discovered that the hydrogen nucleus is present in other nuclei. His experiments showed that nitrogen gas gave signatures of hydrogen nuclei. This hydrogen nuclei could have only come from nitrogen, thus, nitrogen must contain hydrogen nuclei. He named this hydrogen nucleus as proton, which means first.

Neutron

The neutron is a subatomic particle located at the nucleus that has almost the same mass as the proton but has no charge. It was discovered by James Chadwick in 1932. The discovery of neutrons led to the study of nuclear fission and was the particle used to split up the uranium atoms in the first atomic bomb.

The Atomic Theory

THE ATOMIC THEORY

The idea that matter is made up tiny indivisible particles called atomos prevailed for more than 2000 years. This was even noted by Robert Boyle in his book The Sceptical Chymist  and by Isaac Newton in his books Principia and Opticks. But it was John Dalton who proposed the Atomic Theory. Though the idea of the atom wasn’t new, Dalton went further by explaining how atoms combine to form compounds. Dalton expressed his ideas in a series of postules:

John Dalton

1.       Matter is made up of tiny indivisible particles called atoms.

2.       Atoms of a given element cannot be converted into atoms of another element.

3.       Atoms of an element are identical in mass and other properties and are different from atoms of any other element.

4.       Compounds result from the chemical combination of a specific ratio of atoms.

The first and second postulates follow the Law of Conservation of Mass, which states that mass is neither created nor destroyed in an ordinary chemical reaction. Since atoms cannot be cut or destroyed or converted into another atom, its mass is conserved. This also rejects the idea of alchemy’s transmutation. The third and fourth postulates support the Law of Definite Proportion and the Law of Multiple Proportion. The Law of Definite Proportion states that different samples of the same compound always contain its constituent elements in the same proportion by mass. It means that water in France is also the same with water in China – both samples contain two atoms of hydrogen and one atom of oxygen. On the other hand, the Law of Multiple Proportion states that if two elements can combine to form more than one compound, the masses that combine with a fixed mass of the other element are in rations of small whole numbers. For example, chlorine can combine with oxygen to form ClO^-, ClO₂^-, ClO₃^-, and ClO₄^-. This shows that the mass ratio of oxygen combined with chlorine in the four compounds is 1:2:3:4. All values are in whole number ratios.

Since John Dalton believed that an atom is indivisible, his picture of the atom was like of a billiard ball – a tiny particle invisible to the naked eye that does not have smaller components.

History of the Atom

The illustration shows alchemists working in their labs trying to transmute lead into gold and seeking the ultimate goal of alchemy: the Philosopher’s Stone and the Elixir of Life. As alchemists try to understand the nature of matter, they also added significant contributions in the study of medicine.

             For centuries, humans have pondered the origin of his existence. Since time immemorial, we have asked ourselves the question “Where did we come from?” Scientists in the middle ages did several experiments to study the nature of matter but their ideas did not originate from themselves. Greek philosophers have asked the same question and arrived at several answers which we are about to discuss.

 EARLY IDEAS ABOUT THE ATOM

               The chemistry that we know today actually started from the minds of philosophers more than 2000 years ago. But before the conception of science, ancient civilizations never had the idea that they were already using the concepts of chemistry. People knew how to make perfumes, paints, armors made out of metal ores. They also know pottery, baking, and dye-making but they do not know the science behind all of those processes. This period of development of science is called as the period of Practical Arts (---- to 600 B.C.). These processes had no scientific basis and craftsmen only relied on their experiences in making their products.

                         Later on, people started asking questions about what was happening around them. Greeks, in particular, starting studying the philosophical or theoretical aspects of the processes that they were using. This period was called the period of Greek Theory (600 B.C. to 300 B.C.). Below are the list of some noted Greek philosophers and their ideas about the nature and origin of matter:

1.       Thales of Miletus

Thales of Miletus

è
He said that matter came from water. He got this idea when he was surveying the banks of the Nile River. Every time it rains and the Nile Delta overflows, he sees different kinds of plants and animals coming out of the water. He also observed that the soil in the river banks becomes more fertile after the water had subsided. He, therefore, concluded that everything comes from water.

2.       Democritus

Democritus

è
He believed that matter is made up of tiny indivisible particles he called atomos which literally means “uncut” or “indivisible”. He also believed that this atomos should be eternal because everything could be broken down into smaller pieces, then nature would dissolve like constantly diluted soup. Democritus actually got this idea from his teacher Leucippus, but what made his idea different was that he described atomos even further. He said that atomos contains “hooks” and “barbs” that enable them to interact with other particles to form new substances.

1.       Empedocles

Empedocles

è A philosopher from Sicily who believed that matter is composed of four elements, namely: earth, air, fire, and water. He also said that everything around us is made from the the combination of these elements in varying proportions. When you burn a piece of wood, you hear it crackle because of “water” evaporating, we see smoke because of “air”, the “fire” that we can see, and the ash that remains after burning as the “earth”. This idea of the composition of matter became very popular nowadays since a lot of movies make use of this idea as their main theme.

Aristotle

2.       Aristotle

è He believed that matter can be infinitely divided into smaller pieces. He also supported the idea of Empedocles about the four elements.

These philosophical and mystical ideas of the Greeks was combined with the practical arts of the Egyptians in Alexandria which gave birth to a new field of interest for many scientists, the period of Alchemy (300 B.C. to 1650 A.D.). The dominant idea for most alchemists was that base substances, like copper or lead, can be purified with fire and transmute it to form gold. Just like humans, when tested with trials become strong and perfect, matter can also be purified with fire and become the perfect metal during those times, gold. They also believed that if an alchemist was able to transmute a base metal into gold, he can also achieve a very powerful transmuting agent called the Philosopher’s Stone. When alchemy reached the Arabs, they called the Philosopher’s Stone as elixir, the substance that could cure all diseases at give man eternal life by preventing death.

In 1667, a scientist named Johann Joachim Becher postulated that a substance called phlogiston is released when a substance is burned. In 1703, Georg Ernst Stahl, a professor of medicine and chemistry in the University of Halle in Wittenberg, proposed the Phlogiston Theory. According to this theory, when a substance is burned, phlogiston is released into the air and a phlogiston-free ash is left:

Wood à ashes + phlogiston (released into the air)

In the same manner, when a metal is burned, it also releases phlogiston into the air, leaving a phlogiston-free substance called calx.

Metal à calx + phlogiston (released into the air)

One flaw that the Phlogiston Theory supporters was not able to resolve was that when a metal is burned, it should leave a phlogiston-free calx that should weigh less than the metal. But in reality, calx weighs more than the metal. Phlogiston Theory supporters were not able to explain why the calx, which was removed with phlogiston, is heavier than the metal. Nevertheless, this theory dominated most of the eighteenth century until Antoine Lavoisier revolutionized the experimentation process.

Antoine Lavoisier

Antoine-Laurent de Lavoisier, a French Nobleman, debunked the Phlogiston Theory and paved the way for the period of Modern Chemistry (1790 – present). He was able to explain why calx is heavier than its metal by using balances when conducting his experiments. He was also able to do this with the help of Joseph Priestley’s invention of the Oxygen gas. Lavoisier found out that a substance burns, not because phlogiston is released into the air, but because oxygen gas reacts with the substance. In the case of a burning metal, oxygen gas combines with the metal forming a metal oxide, which makes it heavier.

Metal + Oxygen Gas à metal oxide

He also noted that mass is neither created nor destroyed in an ordinary chemical reaction. Thus, the mass of the reactants should also be equal to the mass of the product. This idea is now called the Law of Conservation of Mass. Because of his contributions, he is now called the Father of Modern Chemistry. Sad to say, he was one of the tax collectors who were tried and guillotined during the Reign of Terror in France in 1794.

CONVERSION OF TEMPERATURE

                                The SI unit for temperature is Kelvin, the absolute temperature, named after the engineer and physicist William Thomson, 1^st Baron Kelvin. The two most commonly used units for temperature are Degrees Celsius (°C) named after the Swedish astronomer Anders Celsius, and Degrees Fahrenheit (°F), named after the inventor of alcohol thermometer, Daniel Gabriel Fahrenheit.

                Celsius degree and Fahrenheit degree are not absolute values, which mean that they both have negative values. In converting units of °C to °F and vice versa, we must make use of a standard for reference in comparing the two values, that is, the freezing point and boiling point of water. Water freezes at 0°C and boils at 100°C. In Fahrenheit scale, freezing point of water is 32°F and boiling point is 212°F.

Thus, it takes 180 Fahrenheit degrees to cover the same range as that of 100 Celsius degrees. It means that one Fahrenheit degrees is 100/180 or 5/9 of a Celsius degree and one Celsius degree is 180/100 or 9/5 of a Fahrenheit degree.

                 To convert Celsius degree to Fahrenheit degree, two adjustments must be made;

•   Degree size adjustment
•   Zero-point adjustment

            Degree size adjustment is done by multiplying the given value with the conversion factor, that is,   9°F/5°C  or  5°C/9°F.For the zero point adjustment is done by adding 32°F after converting °C to °F or subtracting 32°F to the given Fahrenheit scale before converting to Celsius degrees.

Example 1: The normal human body temperature is 37°C. What temperature is this in Fahrenheit scale?

Solution: One Celsius degree is equal to 180/100 or 9/5 of a Fahrenheit degree. If you have 37°C, multiply that with 9/5 to get 66.6°F. You need to add 32°F to your answer  for the zero-point adjustment, thus getting 98.6°F.

Example 2: A furnace operates at 1852°F. What temperature is this in Celsius scale?

Solution: You first need to subtract 32°F from 1852°F so that the ranges you are comparing with Celsius scale are the same (starts at zero). One Fahrenheit degrees is 100°C/180°F or 5/9 of a Celsius degree.

Kelvin temperature is an absolute quantity, which means that zero Kelvin is the absence of temperature where atoms and electrons are thought to be immobile. Both Celsius and Kelvin scales have the same magnitude, which means that every Kelvin scale is equal to one Celsius degree 

. According to experimental studies done by Johann Heinrich Lambert in 1779, the approximate value for the absolute temperature is -273.15°C.

SCIENTIFIC NOTATION

                                When solving problems in chemistry, we often come up with very large or very small numbers. For example, 12.9 grams of carbon contains

6.02214150000000000000000 carbon atoms

and each carbon atom has a mass of

0.0000000000000000000000199 g

Having these numbers when solving will make us prone to errors especially in writing those zeros. To avoid missing those zeros, we use scientific notation. 

Scientific notations are written like this:

a x 10^b ( a times ten to the power of b)

where:  a = coefficient  ( any real number between 1 to 10)

               b = exponent 9integer, whole number)

For every large numbers, the exponent is positive while for small numbers, the exponent is negative.

Let’s say you are asked to write 459 000 000 in scientific notation. The first thing to do is to find b. We do this by counting the number of places to decimal point must be moved to get the value of a (that is between 1 to 10).

• The exponent is POSITIVE if the decimal point was moved to the LEFT.
• The exponent is NEGATIVE if the decimal point was moved to the RIGHT.

The following shows how to use scientific notation.

1.                   Write 67940000 in scientific notation

              67940000      =        6.794 x 10⁹

               9 steps to the LEFT          exponent is positive

2.                Write 0.000000000000321 in scientific notation

               0.000000000000321     =    3.21 x 10^-13

               13 steps to the right           exponent is negative

In the example 0.000000000000321, it is not written as 32.1 x 10^-14 or 0.321 x 10^-12 because it will violate the rule the coefficient must be between 1 to 10.

Addition and Subtraction of Scientific Notation

                                When adding or subtracting numbers in scientific notation, we first write each quantity with the same exponent, add or subtract the digits, then copy the exponent.

                                           8.45 x 10⁴                 →             9.2      x 10⁴

                                        + 7.23 x 10³⁽⁺¹⁾       →            0.723 x 10⁴

                                                                                         9.923  x 10⁴

If the coefficient is less than 1 or has two whole number digits, move the decimal point so that the coefficient is between 1. to 10 and adjust the exponent.

                                            9.2 x 10⁷         →        9.2 x 10⁷

                                         + 8.5 x 10⁶         →       0.85 x10⁷

                                                                             10.05 x 10⁷⁽⁺¹⁾ →  1.005 x 10⁸

                                           4.25 x 10^-3         →        4.25 x 10^-3

                                         - 6.15 x 10^-4         →        0.615 x10^-3

                                                                                  3.635 x 10^-3

Multiplication and Division of Scientific Notation

                                When multiplying or dividing numbers in scientific notation, we multiply or divide the coefficient in the usual manner, but add or subtract the exponents.

                                                     2.3 x 10⁴

                                                  x 3.9 x 10⁵

                                              (2.3 x 3.9) (10⁴⁺⁵)   →   8.97 x 10⁹

                                                    5.6 x 10^-4

                                                ÷  4.2 x 10^-2

                                                   (5.6 ÷ 4.2) (10^(-4)-(-2))   →   1.33 x 10^-2

CONVERSION OF UNITS USING FACTOR- LABEL METHOD OR DIMENSIONAL ANALYSIS

                 Many scientific activities and even cultures make use of different units in measuring a specific quantity. These give rise to the necessity of converting those units to a more usable form or more relevant form.

The following are tables showing some conversion factors:

Length Conversion

Metric (SI) to Metric (SI)	English to English	Metric (SI) to English	English to Metric (SI)
1 kilometer = 1000 meter 1 meter        = 100 cm 1 cm              = 10 mm 1mm             = 1000 µm	1 mile = 1760  yard 1 yard = 3 feet 1 foot = 12 inches	1 cm = 0.39 in           1 m = 3.28 ft                   = 1.09 yd.          1 km = 0.62 mi	1 in = 2.54 cm 1 ft. = 30.48 cm 1 yd = 0.91 m 1 mi = 1.61 km

  Mass Conversion

Metric (SI) to Metric (SI)	English to English	Metric (SI) to English	English to Metric (SI)
1 metric ton = 1000 kg 1 kg = 1000 g 1 g = 1000 mg	1 ton = 1000 lbs. 1 lb = 16 ounces	1 metric ton = 1.01 ton        = 2204.62 lbs 1 kg = 2.2 lbs 1 g = 0.035 ounce	1 ton = 0.90 metric ton            = 907.2 kg 1 lb = 0.454 kg 1 ounce = 28.35 g

    

Volume Conversion

Metric (SI) to Metric (SI)	English to English	Metric (SI) to English	English to Metric (SI)
1 m3 = 1000 L 1 L = 1000 mL       = 1000 cm3 1 mL =  1 cm3	1 ft3 = 1728 im3                  = 7.48 gallons 1 in3 = 16.39 mL  1 gallon(gal) = 4 quarts 1 quart(qt) = 2 pint 1 pint = 16 fluid ounce 1 fluid ounce(oz) = 2 tbsp. 1 tbsp. = 3 tsp.	1 m3 = 35.31 ft3                  =  264.17 gal         1 L = 0.26 gal                = 1.06 quart 1 mL = 0.07 tbsp	1 ft3 = 28.31 L 1 in3 = 16.39 mL 1 gal = 3.79 L 1 quart = 0.95 L 1 pint = 0.47 L 1 tbsp. = 14.79 mL

Suppose for example, you have your height measured in feet, let’s say 5 feet. Your application form requires you to write your height in meters. How do you convert your height from feet to meters?

The conversion factor that we need to solve the problem is derived from this relationship:

1 foot = 0.3043 m

From this relationship, we can derive two conversion factors by dividing both sides by either of the two:

                  

The factors are equivalent to 1 since the numerators and denominators are equivalent.

To convert 5 feet to meters, multiply the given to the conversion factor that can cancel out the undesired unit to come up with the meters.

                Factor-Label Method or Dimensional Analysis does not change the value of the given quantity. Since the conversion factor is equal to 1, the process only changes the unit.