R3 Atomic Concepts Kathleen - Miller Place High School

Atomic Concepts

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Atomic Concepts 2 nyschemistry.net

Atomic Concepts Table of Contents

1.0 The Mystery of the Atom .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.0 Dalton’s Atomic Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

3.0 The Discovery of Atomic Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

3.1 The Discovery of Electr ical Charges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

3.2 The Cathode Ray Tube . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

3.3 The Plum-Pudding Model of an Atom .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

3.4 Goldstein’s Canal Rays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

3.5 Mil l ikan’s Oil Drop Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

3.6 X-rays Detected . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

3.7 Radioact iv ity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

3.8 The Alpha-Scatter ing Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

3.9 The Neutron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

3.10 The Subatomic Part ic les . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

3.11 Atomic Number and Mass Number . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

3.12 Isotopes and Atomic Masses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

4.0 The Electronic Structure of Atoms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

4.1 The Electromagnetic Radiat ion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

4.2 Atomic Spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

4.3 Planck’s Quantum Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

4.4 The Bohr Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

4.5 The Photoelectr ic Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

4.6 The Wave-Part ic le Dual ity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

4.7 Heisenberg’s Uncertainty Principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

4.8 The Quantum Mechanical Model of an Atom .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

4.9 The Four Quantum Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

4.10 Electron Configurat ion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

5.0 Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3 Atomic Concepts nyschemistry.net

1.0 The Mystery of the Atom

The concept of the atom started in the ancient world of the Greek philosophers. It was Leucippus of Miletus and his student Democritus (460-370 B.C.) who preconceived the concept of the atom at around 440 B.C. However, Aristotle, the renowned Greek philosopher, opposed it, together with Cicero, Seneca, and Galen. Hero of Alexandria (150 A.D.) used the atoms to explain compression and refraction. He believed that a vacuum existed between atoms in any flammable material, allowing fire to penetrate it. Diamond, being the hardest stone, cannot catch fire because there is no vacuum. This was later proven by experiments.

The church, too, joined in the battle of ideas in atomism. Belief in atomism at that time was equated to atheism.

The word “atom” came from the Greek word “atomos”. It means “uncuttable.” Democritus raised some important points regarding the atom.

1. All matter is composed of atoms.

2. These atoms cannot be further divided into smaller portions.

3. There are empty spaces between atoms.

4. Atoms are completely solid.

5. Atoms are different in sizes, shapes, masses and positions.

Plato and his student Aristotle thought otherwise because they considered atomism as a challenge to their god. Aristotle refused the idea that the natural world could be reduced to random assortment of atoms moving through a vacuum.

The revival of atomic thinking started with the invention of the barometer by Evangelista Torricelli (1634). His observation of the space above the mercury in a barometer was a proof of the existence of a vacuum which Aristotle refused to believe. The existence of atoms was further supported by Jeremias Benjamin Richter (1976-1807), who proposed the Law of Definite Proportions in 1792. He found out that the ratio by weight of compounds produced and formed in a chemical reaction was always the same. Richter used the Law of Definite Composition (1794) and Isaac Newton’s concept of the atom to explain and justify his discovery.

Meanwhile, Francis Bacon believed that the formation of a new substance is due to the arrangement of tiny visible parts. At the turn of the 19th century, experiments with gases led John Dalton (1803) to propose his atomic theory. Eventually, the debate on the existence of atoms ceased and the concept of the atom became universally accepted.


2.0 Dalton’s Atomic Theory

John Dalton (1766-1844) was a chemist and a physicist who is known as the Father of Modern Atomic Theory. The following were his assumptions about the atom.

1. Each element is composed of extremely small particles called atoms.

2. All the atoms of a particular element are identical in mass, size, shape, and other properties.

3. Atoms of one element cannot be changed into atoms of other elements or be destroyed in chemical reactions.

4. Atoms combine in a definite ratio to form a compound.

5. The relative numbers and kinds of atoms in a given compound do not change.

Dalton’s assumptions were accepted without challenge during his time. The inconsistencies in his assumptions were noted only later. Atoms are not indivisible at all because they can undergo fission during nuclear reaction. Moreover, atoms of the same element may have different masses such as those in isotopes. With regard to the atom’s indestructibility, it should be noted that in a nuclear reaction, the atomic mass of the atom is totally changed by yielding an entirely different atom or isotope.

Dalton’s theory explains several simple laws of chemical combination that were known in his time. One of these was the Law of Constant Composition: In a given compound, the relative numbers and kinds of atoms are constant. This is the basis of Dalton’s postulates 4 and 5. Another fundamental chemical law was the Law of Conservation of Mass: The total mass present after the reaction is the same as the total mass before the reaction. This is the basis of postulate 3. Dalton used his theory to deduce the Law of Multiple Proportions: If two elements A and B combine to form a new compound, the masses of B that can combine with a given mass of A are in a ratio of small whole numbers. As an example, let’s look at water (H2O) and hydrogen peroxide (H2O2). In water, 2 atoms of hydrogen combine with 1 atom of oxygen. In hydrogen peroxide, 2 atoms of hydrogen combine with 2 atoms of oxygen. We can conclude that hydrogen peroxide contains twice as much atoms of oxygen as water does.


3.0 The Discovery of Atomic Structure

3.1 The Discovery of Electrical Charges

Thales of Miletus serendipitously discovered that when amber, a fossilized resin from pine trees, was rubbed against a piece of fur, it attracts light objects. Plato called this resin “electron”, a Greek word for amber. Sir William Gilbert used the term “electron” for a body that attracts in the same way as amber did. Benjamin Franklin believed that only one kind of electric fluid is present in all bodies. An object picks up an electric charge when some of this fluid is transferred from one body to another. He also believed that frictional force causes some positive and negative charges to transfer from one material to another. He thought that the positive charges are the ones capable of transferring. Modern scientists have evidences that it is the negative charge that transfers from one body to another rather than the positive charge. Charles-Agustin de Coulomb made a quantitative measurement on charges of equal magnitude and showed that force is inversely proportional to the square of the distance between charged particles. This is known as the Coulomb’s Law.

F = k

In the formula above, the symbol F represents the coulombic potential energy, k is a constant and d is the distance between the charged particles. Q1 and Q2 denote the magnitude of the charges of the two particles. This shows us that if charged particles are far from each other, their attractive or repulsive force on each other is less.

3.2 The Cathode Ray Tube

The British physicist Sir Joseph John Thomson performed several experiments on the cathode ray tube or CRT. It is a partially evacuated glass tube with both positive and negative electrodes. When electric current was passed through the CRT, a ray radiated and struck the phosphor-coated end. A flash of light was emitted. Since the ray originated from the negative electrode (cathode) and moved to the positive electrode (anode), it was named cathode ray. It was later identified as a stream of electrons. The cathode rays travelled in straight lines but were deflected by electric and magnetic fields. The cathode ray was deflected towards the positive electrical plate. The direction of the deflection confirmed that it behaved like a negatively-charged particle because it was attracted to the positive electrical plate. Thomson replicated his experiment and obtained consistent results. He was able to determine the electric charge-to-mass ratio (Q/m) of an electron. He found this value to be approximately equal to -1.759 x 108 coulombs per gram (C/g). The discovery of the electron was credited to Thomson.


Figure 3.1 Cathode ray tube with perpendicular electric and magnetic fields. The cathode rays originate from the negative plate on the left and are accelerated toward the positive plate, which has a hole (C) in its center. The beam of electrons passes through the holes (A and B). It is then deflected by the electric and magnetic fields. It was deflected away from the negatively-charged plate (O) and towards the positively-charged plate (E).

3.3 The Plum-Pudding Model of an Atom

With Thomson’s discovery of the electrons, he proposed a structure for the atom—the Plum-Pudding Model. Each atom is a sphere filled with a positively charged fluid—tthe “pudding.” Embedded in it are the fluid electrons–the “plums.”

Figure 3.2 The Plum Pudding Model of an atom.


3.4 Goldstein’s Canal Rays

In his experiment with a CRT, Eugene Goldstein used a perforated cathode and he observed that aside from the cathode rays, some particles passed through the cathode perforations. These struck the fluorescent coating. He called these as canal rays because they passed through the canals or perforations of the cathode. He further hypothesized that these particles are what are left when electrons are removed. He proved that canal rays are actually stream of positively-charged particles. Thus, the discovery of the positively-charged subatomic particle (proton) is credited to him.

Figure 3.3 Goldstein’s experiment with a

cathode ray tube.

3.5 Millikan’s Oil Drop Experiment

In 1913, Robert Andrews Millikan measured the charge of an electron through an apparatus containing electrically charged plates and an X-ray source. This was called the oil-drop experiment. He sprayed a mist of high grade oil inside to pass through the hole at the upper positive plate. The X-ray knocked off the electrons from the air inside. The electrons stuck up with the oil drop, giving it a negative charge. He found that the charge of every oil drop was a multiple of 1.602 x 10-19 C (coulomb). He concluded that this was the magnitude of the charge of an electron. In recognition of this important contribution, he was awarded the 1923 Nobel Prize in physics. By combining his findings with Thomson’s experimental results, the mass of the electron was calculated. This mass is 2000 times lighter than the mass of a hydrogen atom, the lightest atom.

= -1.76 x 108 C/g

Q = -1.602 x 10-19 C

m =

€

QQm

=

€

-1.602 x 10-19 C-1.76 x 108 C/g

= 9.10 x 10-28 g

Q/m = charge to mass ratio

Q = magnitude of the charge of an electron

m = mass of an electron

The mass of an electron is 9.10 x 10-28 g.


Figure 3.4 Millikan’s Oil Drop Experiment

3.6 X-rays Detected

In 1895, the German physicist Wilhelm Conrad Roentgen accidentally discovered an unknown radiation while studying cathode rays using a high-voltage discharge tube. He encased this tube in a black cardboard box. He noticed that a barium-platinocyanide screen lying nearby emitted fluorescent light each time the tube was in operation. Roentgen conducted further experiments. He was able to determine that the fluorescence was caused by an invisible radiation. He called this as X-ray because of its unknown nature. Today, X-rays are used in the field of scientific research, medicine and the industry.

3.7 Radioactivity

Knowledge about radioactivity started with the discovery of X-rays. Henri Becquerel and Marie Curie, through their studies, learned that some elements give off radiation spontaneously. Radioactivity is defined as the spontaneous emission of radiation by radioactive materials. Radiation is a form of energy transmitted as waves. Both Marie Curie and her husband, Pierre Curie identified several radioactive elements. Ernest Rutherford, through the assistance of Johannes Wilhelm Geiger and Ernest Marsden, was able to identify the different types of radiation, the alpha and the beta. Alpha (α) radiation consists of helium atoms. The beta (β) radiation is made up of high speed electrons. The third type is the gamma (γ) radiation, which was discovered by Paul Ulrich Villard in 1900. Of the three types of radiation, the alpha particle has the least penetrating power. The gamma rays are the most penetrating. These have very short wavelengths and high energies. These cannot be stopped by any shielding material as easily as the alpha and beta radiations because they carry no charge.


Figure 3.5 The penetrating power of the alpha (α), beta (β) and gamma (γ) rays.

3.8 The Alpha-Scattering Experiment

Ernest Rutherford, with Geiger and Marsden, determined the deflection that the alpha particles will exhibit on a thin gold foil. This thin gold foil contained approximately 100 gold atoms. Most alpha particles passed through undeflected. Some were deflected, while a few bounced back. Based on these results, Rutherford proposed an atomic model. The following postulates were established.

1. Most of the atom is empty space. This caused most of the alpha particles to pass through undeflected.

2. Most of the mass and all of the positive charges of an atom are centered in a very small region called the nucleus. This explains the bouncing back of a few alpha particles. Those few alpha particles hit the massive, positively charged nucleus. The alpha particles, being positively charged, were repelled by the nucleus. The deflected alpha particles passed by near the nucleus. They were slightly repelled.

3. There exist as many electrons outside the nucleus as there are units of positive charges on the nucleus.

The discovery of the nucleus and the protons was credited to Rutherford.


Figure 3.6 The Alpha Scattering Experiment

With his discoveries, Rutherford proposed a structure of an atom. His model of an atom is mostly empty space wherein all positive charges reside at its center called the nucleus. Hovering around are the negatively-charged electrons.

Figure 3.7 Rutherford’s model of an atom.

3.9 The Neutron

Rutherford proposed that the mass of an atom is concentrated in its central part. Since this is also the location of the protons, he hypothesized that the mass of an atom is the total mass of the protons. Henry Gwyn Moseley discovered through his experiments that the mass of an atom is not equivalent to the mass of the protons. He hypothesized that there must be other particles in the nucleus that contain no charge but possess mass. James Chadwick verified by bombarding beryllium compounds with alpha particles that there is found in the nucleus another


particle besides the proton. He called this particle as neutron. It has a mass of 1 atomic mass unit but has no charge.

3.10 The Subatomic Particles

The experiments on CRT have proven that the atom has substructures. The nucleus is composed of the protons (p+) and the neutrons (n0). The number of protons in the nucleus is balanced by the number of electrons surrounding the nucleus. These electrons (e-) are held by the attractive force of the protons in the nucleus. The proton has a charge of +1, The electron has -1 and the neutron has none.

Table 3.1 Comparison of the subatomic particles

Particle Charge Mass (amu)

Proton +1 1.0073

Neutron 0 1.0087

Electron -1 5.486 x 10-4

3.11 Atomic Number and Mass Number

The atomic number represents the number of protons in the nucleus of an atom. In a neutral atom, the number of positively charged particles is equal to the number of negatively charged particles. That is, the number of protons is equal to the number of electrons. An element is represented by , where X is the symbol for the element, Z is the atomic number and A is the mass number. The mass number is the sum of the number of protons and the number of neutrons. The contribution of the electrons to the mass of the atom is negligible. The mass of the atom only depends on the neutrons and the protons. Let’s have sodium as an example. The sodium atom can be represented as . The atomic number (Z) is 11 and the mass number (A) is 23. Let’s obtain the number of protons, electrons and neutrons.

Z = 11 Z = p+ = e- p+ = 11 e- = 11 A = 23 A = p+ + n0 n0 = A – p+ = 23 – 11 = 12

A sodium atom has 11 protons, 11 electrons and 12 neutrons.


3.12 Isotopes and Atomic Masses

The atoms of a given element may have different masses. The difference in the masses is attributed to the number of neutrons. Atoms of the same element having the same number of protons but different number of neutrons are called isotopes. Different isotopes of an element have different stabilities. Thus, they also have different amounts, called percent abundances. The most stable isotope has the greatest percent abundance. Hydrogen for example has three occurring isotopes. They are protium, deuterium and tritium.

Figure 3.8 Hydrogen has three isotopes: protium, deuterium and tritium.


Figure 3.9 The Modern Periodic Table


By convention, an isotope is differentiated from other isotopes by incorporating in the name or symbol the mass number. Protium has a mass number of 1 and an atomic number of 1 as well. It is represented as . Deuterium is represented as and tritium as . Or, they can also be simply represented as H-1 (read as hydrogen one), H-2 (read as hydrogen two) and H-3 (read as hydrogen three), respectively.

Table 3.2 The Properties of The Isotopes of Hydrogen

Isotope Name Z p+ e- n0 A %Abundance

Protium 1 1 1 0 1 99.985 %

Deuterium 1 1 1 1 2 0.0115 %

Tritium 1 1 1 2 3 Trace

The average masses of all the isotopes of an element considering their percent abundances are referred to as the average atomic mass of the element. As a result, atomic masses are not whole numbers. Atomic mass is expressed in atomic mass unit (amu). The average atomic mass is the mass that appears in the periodic table.

The relative abundances of the silicon isotopes and their masses are given in the table below. Compute for the average atomic mass.

Table 3.3 The Isotopes of Silicon

Isotope Isotopic Mass (amu) Relative Abundance

Si-28 27.98 92.21 %

Si-29 28.98 4.70 %

Si-30 29.97 3.09 %

To get the average atomic mass, we sum up the product of the isotopic masses and their corresponding relative abundances. In other words, it is the summation of the products of the masses and the abundances.

Ave. Atomic Mass = Σ(isotopic mass)(%abundance)

Example:

Ave. atomic mass of silicon = (27.98 amu)(92.21%) + (28.98 amu)(4.70%) + (29.97 amu)(3.09%)

Ave. Atomic mass of silicon = 28.09 amu


4 .0 The Electronic Str ucture of Atoms

4.1 The Electromagnetic Radiation

Electromagnetic radiation is a form of energy transmission through a vacuum (empty space) or a medium (such as glass) in which electric and magnetic fields are propagated as waves. In 1873, James Maxwell proposed that visible light is a kind of electromagnetic wave. All electromagnetic waves travel in the speed of 3.0 x 108 m/s, the speed of light in a vacuum.

The visible light makes up only a small portion of the whole electromagnetic spectrum. The electromagnetic spectrum of an object is the characteristic distribution of electromagnetic radiation emitted or absorbed by that object. An instrument used to examine the spectrum of objects is known as a spectroscope. The spectroscope uses glass prism through which visible light passes through and breaks into different colors (from violet to red) of different wavelengths. The spread of colors from one end to another end of the electromagnetic spectrum is determined by the amount of energy emitted. This is measured in terms of wavelength. An example of a spectrum is a rainbow. It is a continuous spectrum in which the colors are connected to each other. There are no breaks in between. The rainbow is actually sunlight that is separated into different colors when the fine water droplets in the sky act as a prism.

Figure 4.1 shows a diagram of a wave. The crest is the highest point of the wave while the trough is its lowest point. A wavelength is the distance between two consecutive crests or troughs. Moving waves can be described by their frequency as well as by their wavelength. The amplitude of a wave is the distance between the highest or lowest point of a wave to its midpoint. The frequency is number of cycles of a wave that passes through a certain point. It has the unit s-1 (per second) or hertz. The speed of light (c), wavelength ( ) and frequency ( ) are related by

c = =

Long wavelength means low frequency while short wavelength means high frequency.

Figure 4.1 The Wave


Figure 4.2 The Characteristic Wavelengths of the Different Colors of the Spectrum

4.2 Atomic Spectra

When an element or compound is vaporized through an external heat source, it emits light that when viewed through a spectroscope forms a series of lines. These lines correspond to certain wavelengths or energy emitted. An electron in an atom is said to be in its ground state. This is the state of lowest energy. When an atom absorbs energy due to heating for example, its electrons jump to higher energy levels. The atom is said to be in an excited state. This is an unstable state for the atom. Eventually, the electrons will return to its ground state and the absorbed energy will be emitted.

The emitted energy will be seen as light with characteristic colors. Through a spectroscope, it is seen as a series of fine lines of individual colors separated by black spaces. This is known as the atomic or line spectra. Each color has its own wavelength and has different amounts of energy. Gaseous substances produce line spectra. Only one spectral line is formed by each element. This provides a means of identifying the element. Sodium emits an intense yellow light. Strontium emits a red color. Potassium has purple, barium has green and calcium has red orange. The color displayed by each atom simply signifies the energy absorbed by the atom during excitation.


Figure 4.3 The Spectrum of Hydrogen

4.3 Planck’s Quantum Theory

The bright light of tungsten light bulb or the red glow of an electric heater is a manifestation of radiation from solids. According to Max Karl Ernst Ludwig Planck, atoms and molecules could emit or absorb energy only in discrete quantities like small “bundles”. He gave the name “quantum” to the smallest quantity of energy that can be emitted or absorbed in the form of electromagnetic radiation. The energy of an emitted quantum is proportional to the frequency of the radiation. Planck’s equation is

E = h

Where: E = energy

= frequency of light h = Planck’s constant = 6.63 x 10-34 J-s (Joule-second)

Planck’s equation is also related to wavelength. From the properties of light,

c =

=

Substituting the above equation to Planck’s, we have

E = h

This tells us that the energy and wavelength are inversely proportional. Waves with short wavelengths correspond to higher energies. Waves with longer wavelengths have lower energies.


4.4 The Bohr Model

The Rutherford model of an atom does not provide plausible explanations for the observed line spectrum of elements through a spectroscope. It also does not indicate how electrons are arranged outside the nucleus of an atom. According to classical physics, stationary negatively charged electrons would be pulled into the positively charged nucleus. This suggests that the electrons in an atom must be in motion, like the orbiting motion of planets around the sun. However again, according to classical physics, orbiting electrons should be constantly accelerating and should radiate energy. By losing energy, the electrons would be drawn even closer to the nucleus. This will cause a collapse of the atom. In 1913, Neils Bohr resolved this dilemma using Planck’s quantum hypothesis. In a blend of classical and quantum theory, Bohr postulated that for a hydrogen atom.

1. The electron moves in circular orbit about the nucleus.

2. The electron only has a fixed set of allowed orbit called stationary state. As long as the electron stays in the given orbit its energy is constant and no energy is emitted.

3. An electron can pass only from one allowed orbit to another. In such transitions, fixed discrete quantities of energy called quanta are involved.

Figure 4.4 Bohr’s Model of the Atom

Normally, the electron in a hydrogen atom is found in the orbit closest to the nucleus. This is the lowest allowed energy, or the ground state. When electrons gain a quantum of energy, it moves to a higher level and the atom is in an excited state. When the electron drops from a higher energy level to a lower energy level, a unique quantity of energy is emitted. This amount of energy emitted is the difference in energies of the higher and lower levels.

The great value of the Bohr’s theory was in providing a simple model for interpreting the atomic spectrum of hydrogen and hydrogen-like species such as He+ and Li+2. They all have one electron. It does not however do a good job in predicting the spectra of multielectron atoms. For this, a new quantum theory is needed.


4.5 The Photoelectric Effect

The photoelectric effect explains the observation that when light of sufficient energy shines on a metal surface, electrons are knocked off or ejected. It thereby produces an electric current. This phenomenon was observed by Albert Einstein. This observation cannot be explained by the wave theory of light. According to Einstein, a beam of light should not be thought to be in the form of waves but as a stream of particles called photons. He used Planck’s Quantum Theory as a baseline to deduce that each photon must possess energy, as in

E = mc2

Where:

E = energy m = mass c = speed or velocity of light = 3.0 x 108 m/s

Mass is a property of a particle and not of a wave. The photoelectric effect proved that light has a particle-like property. For his explanation of the photoelectric effect, Einstein won the Nobel Prize for physics in 1921.

Figure 4.5 The Photoelectric Effect

4.6 The Wave-Particle Duality

The wave-particle duality of matter was proposed by the French student Louis Victor de Broglie in 1924. Although old experiments showed that matter is a particle and energy is a wave, it seemed that matter (such as an electron) has a wave nature and photons (energy) have a particle nature. The electrons and the photons show both the behavior of a particle and a wave. This theory of dual character is known as the Wave-Particle Duality. De Broglie’s doctoral thesis assumed that light has both the properties of a particle and a wave. He extended this idea to electrons. A particle in motion as it moves through space has its energy proportional to its mass and the speed (s) of its motion. Einstein’s equation E = mc2 refers to the properties of light. When used for any matter, it becomes E=ms2, where s is the speed of a particle in motion. Incorporating it with Planck’s equation, it becomes


ms2 = =

This tells us that the wavelength and the mass are inversely proportional to each other. De Broglie concluded that wave properties cannot be exhibited with particles having heavy masses. But if the mass of an object is negligible, such as that of an electron, then it will exhibit both particle and wave properties.

4.7 Heisenberg’s Uncertainty Principle

Werner Karl Heisenberg proposed the Uncertainty Principle. This states that we cannot measure position and momentum with great precision simultaneously. If the electrons are moving in a wave-like motion, it is not possible to determine with great precision its position and momentum at the same time. We can know however only one condition or the other but never both.

4.8 The Quantum Mechanical Model of an Atom

This model of the structure of an atom was proposed by Erwin Rudolf Josef Alexander Schrödinger in 1926. This is the result of the incorporation of the particle-wave concept of de Broglie and Heisenberg’s Uncertainty Principle. He derived an equation using quantum mechanics (a higher form of mathematics) that was the basis for the quantum mechanical model of an atom. The results of his calculations are called the quantum numbers. They are mathematical parameters in describing the most probable location of electrons around the nucleus of an atom. Schrödinger was able to come up with three quantum numbers. They are the Principal Quantum Number, The Azimuthal Quantum Number and the Magnetic Quantum Number. When specific values are assigned to these three quantum numbers, the resulting wave function is called an orbital. An orbital is a region in an atom where an electron is most probably found. It is different from an orbit.

Figure 4.6 The Quantum-Mechanical Model of an Atom


4.9 The Four Quantum Numbers

1. Principal Quantum Number (n)

This describes the size of an atom and the energy an electron has. This also indicates the relative distance of an electron from the nucleus. This has values of positive integers 1, 2, 3, and so on. The value n=1 is the 1st energy level. This is the lowest energy level and the closest to the nucleus. An electron in the 1st energy level therefore has the lowest amount of energy and it is also tightly held by the nucleus. The energy levels are also called shells.

2. Angular Momentum Quantum Number or Azimuthal Quantum Number ( )

This refers to the shape of the orbitals. It has values of 0, 1, 2, 3 ... (n-1). The different values of correspond to the different sublevels or subshells in an energy level. They also have different shapes. The shell n=1 has = 0. With reference to the table below, this means that the 1st energy level has the s subshell. The 2nd energy level or n=2 has two values, 0 and 1. This means that the 2nd energy level has both the s and p subshells. The 3rd energy level has the subshells s, p and d while the 4th energy level has s, p, d and f. This is summarized in table below.

Table 4.1 The Values and Their Corresponding Shapes

value sublevel Shape of orbital 0 s (sharp) Spherical 1 p (principal) Dumbbell-shaped 2 d (diffuse) Clover 3 f (fundamental) More complex than d

Table 4.2 The Subshells in the Shells

Energy level, n subshell # of subshells 1 0 s 1

0 s 2 1 p

2

0 s 1 p 3 2 d

3

0 s 1 p 2 d

4

3 f

4


3. The Magnetic Quantum Number (m )

This refers to the orientation of the orbitals in space around the nucleus. It has values of - through 0 to . Each m value has a corresponding orientation in space. For = 1, the m values are -1, 0 and 1. This also means that the s subshell has three orbitals with different orientations. For

= 2, the m values are -2, -1, 0, 1, 2. Five orbitals with different orientations exist for the d subshell. The names of the orbitals are the same as with the subshell in which they appear. The number of m values for a given is equal to the number of orbitals in that subshell. It can be then said that the s subshell has one s orbital. The p subshell has three p orbitals. The d subshell has five, and the f has seven. The number of orbitals in a subshell is 2 +1. This also indicates the number of orbitals in a given energy level. It is given by n2.

Table 4.3 Summary of the Number of Orbitals

n m Number of orbitals

(2 +1) Total number of orbitals (n2)

1 0 0 1 1 0 0 1 2 1 -1, 0, 1 3

4

0 0 1 1 -1, 0, 1 3 3 2 -2, -1, 0, 1, 2 5

9

0 0 1 1 -1, 0, 1 3 2 -2, -1, 0, 1, 2 5

4

3 -3, -2, -1, 0, 1, 2, 3 7

16

4. Spin Quantum Number

This describes the spins of the electrons which are in opposite directions to differentiate one electron from the other in an orbital. The spin quantum number has two values, +½ (clockwise spin) and -½ (counter clockwise spin).

4.10 Electron Configuration

Electron configuration is the distribution or arrangement of electrons in the energy levels and sublevels of an atom. It is represented by n #. The n is the energy level, is the sublevel, and the number sign # is the number of electrons occupying the orbital. The distribution of electrons is made simpler by the use of a mnemonic device. The electrons occupying the highest or the outermost (valence) energy level are known as the valence electrons. The inner electrons are more commonly known as the core electrons.


Figure 4.7 The Mnemonic Device

The following are the rules that govern the distribution of electrons in an atom.

1. Aufbau Principle

Aufbau is a German word that means “building up”. This states that electrons are added to an atom starting from the lowest energy level orbital. Hence the 1st energy level is filled with electrons first before assigning an electron to the 2nd energy level.

2. Pauli’s Exclusion Principle

This was proposed by Wolfgang Pauli in 1926. This states that only two electrons of opposite spins can occupy a single orbital. Opposite spins minimize electrostatic repulsion. With this, the maximum number of electrons in an energy level is given by 2n2. The 1st energy level can accommodate a maximum of only two electrons. The 2nd energy level can accommodate a maximum of eight.

3. Hund’s Rule of Multiplicity

This was proposed by Friedrich Hund. This states that for degenerate orbitals, electrons distribute singly first before pairing. Orbitals with the same energy are said to be degenerate. Examples of degenerate orbitals are the px, py, and pz, and the five d orbitals.

An electron configuration can also be represented by an orbital box diagram. The orbitals are represented by boxes. An electron spinning clockwise is represented by an arrow up; an arrow down is for an electron spinning counter clockwise.

According to Wolfgang Pauli, no two electrons may have the same values for all the four quantum numbers. This is known as the Pauli Exclusion Principle. It also implies that only two electrons may occupy the same orbital and these electrons must have opposing spins. As an example let us take a look at a carbon atom. It has six electrons. Its electron configuration is 1s22s22p2. The 1st two electrons have the same values of n, , and m but different ms values. Let us try distributing the electrons of carbon. Carbon has an atomic number (Z) of 6. Therefore, it has 6 electrons.


Figure 4.8 is the orbital box diagram for the electron configuration of carbon. The 1st energy level can accommodate a maximum of only 2 electrons. According to the Aufbau Principle, it has to be filled first before distributing an electron to the next energy level. The 2nd energy level can hold a maximum of 8 electrons. Its s subshell can hold 2 electrons and its p subshell can hold a maximum of 6. The s subshell has to be filled first. When the 1st energy level and the s subshell of the 2nd energy level are filled with electrons, 2 electrons remain undistributed. They have to occupy the p subshell of the 2nd energy level. According to Hund’s Rule of Multiplicity, the degenerate orbitals have to be filled singly first before they will be paired with electrons. In the case of carbon, 1 electron occupies the 1st p orbital and 1 occupies the 2nd. It should be noted that when two electrons occupy a single orbital, they have opposite spins. Again, this is to minimize repulsion. The 2 electrons occupying the degenerate orbitals of carbon have the same spins. This is because the two of them occupy different orbitals. But when some more electrons will be added such that the degenerate orbitals hold 2 electrons each, the added electron will have a spin opposite to the spin of the already existing electron.

Figure 4.8 Orbital Box Diagram for Carbon

The valence electrons and the core electrons are sometimes differentiated from each other. This is seen in a condensed electron configuration. In this form, the core electrons are represented by the symbol of a noble gas and the valence electrons with the spdf notation. In this form, the electron configuration of carbon is [He]:2s22p2. The noble gas helium has 2 electrons. Its electron configuration is 1s2. The outermost energy level of the carbon atom is the 2nd energy level. Since there are 4 electrons (2 in the s and 2 in the p subshell) occupying that outermost level, carbon has 4 valence electrons. The figure below shows the subshells in which the valence electrons of the atoms in the periodic table occupy.

Figure 4.9 The periodic table and the subshells of the valence electrons of atoms


5.0 Quiz

I. Give the electron configuration of the following atoms.

1.

2.

3.

4.

5.

II. Complete the Table

A. Electron Configuration and the Subatomic Particles

Atom

p+ e- n0 Z A Valence e-

6 6 6 6 12 4

16 32

19 39

20 40


B. The Quantum Numbers

Quantum Numbers Electron e- configuration

n m ms

The last entering e- in boron 1s22s22p1 2 1 -1 +½

The 5th entering e- in carbon

The 1st entering electron in chlorine

III. Identification

1. ____________________ proposed that matter and wave can have dual nature.

2. According to ____________________, degenerate orbitals are filled with electrons singly

first.

3. Radioactivity was first discovered by the observation of a/an ________________. It was

named as such because of its unknown nature.

4. The solutions to the equations of Schrödinger are collectively known as _______________.

5. The discovery of the electrons was attributed to _________________. He was also given

credit for the discovery of ________________.

6. The _____________________ states that matter cannot be created nor destroyed. It can

only change its form.

7. In the ____________________________, alpha particles are bombarded to a thin gold foil.

It was found out that something massive and positively charged is at the center of the

atom.

8. The arrangement of electrons in an atom is guided by rules. This arrangement is also

known as the _________________ of an atom.

9. The number _________________ in an atom is the difference between the mass number

and the number of neutrons.

10. The sodium atom has 11 electrons. It also has ___________ protons.

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R3 Atomic Concepts Kathleen - Miller Place High School