## Unit 2 Study Guide: The Atom

### 2a. Define the atom

• How do we define the atom?

All matter is made up of small particles known as atoms.

John Dalton (1766-1844), an English chemist and physicist, introduced the concept of atoms in the 1800s. Atoms are the fundamental unit of all matter. They consist of subatomic particles known as protons, neutrons, and electrons. However, we cannot break atoms apart, except during a nuclear reaction. During a chemical reaction, atoms are rearranged, but they are not destroyed or changed.

Note that an element is a specific type of atom that has a unique set of properties. The elements are what are found on the periodic table. For example, the elements hydrogen, helium, carbon all have different atom types.

### 2b. List the properties of protons, neutrons, and electrons

• Describe the properties of protons, neutrons, and electrons.
• Which subatomic particles exist in the nucleus of the atom?
• Draw a simple diagram of the nuclear atom.
• How are ions formed?
• What is a quantum particle?

All atoms contain subatomic particles known as protons, neutrons, and electrons. These subatomic particles have different properties.

Scientists have identified three particles within an atom:

1. Protons exist in the nucleus (or dense center) of the atom, where almost all of the mass of the atom is contained. Protons and neutrons have approximately the same mass. Protons have a positive charge.
2. Neutrons exist in the nucleus of the atom with the protons. Protons and neutrons have approximately the same mass. Neutrons have no charge.
3. Electrons exist in the atom as an electron cloud that surrounds the nucleus of the atom. We consider electrons "quantum particles" because they have almost no mass. We also cannot determine an electron's exact location at any given time. We can only determine the probability of finding an electron at a given location at a given time. Electrons have a negative charge.

When atoms that have no charge, an equal number of protons and electrons exist to create a neutral charge.

Ions describe atoms that have a negative or positive charge. These ions, or "charged particles", have a negative charge when the number of electrons is greater than the number of protons, or a positive charge when their protons outnumber the electrons.

### 2c. Define isotopes and explain how they relate to naturally occurring element mass

• Describe isotopes.
• Use isotope notation to write the symbol for an isotope.
• How do we determine average element mass based on isotopes?

Isotopes are atoms of the same element that have different masses.

We define an element by the number of protons it contains. For example, hydrogen atoms (represented by a capital letter "H") have only one proton.

However, atoms that are the same element (by definition they have the same number of protons) can have different numbers of neutrons. We call atoms that are the same element, but have different numbers of neutrons, isotopes. So for example, you can have different isotopes of hydrogen, which will have a different mass due to the different numbers of neutrons.

We can write symbols isotopes in terms of two important quantities: atomic number (which scientists represent in their equations with the capital letter "Z") and mass number (which scientists represent in their equations with the capital letter "A").

• The atomic number of an atom is the number of protons that exist in the element (and defines the element). You can find the atomic number for every element listed on the periodic table.
• The mass number of an isotope is the sum of the number of protons and neutrons.

We can calculate n + Z = A, with n being the number of neutrons (in other words, neutrons + atomic number = mass number). Turn this equation around and you can subtract the atomic number ("Z") from the mass number ("A") to determine how many neutrons exist in the isotope.

Scientists write the symbol for an isotope (with the mass number and atomic number) this way:

This image offers another example of how isotope symbols are written for the isotopes of hydrogen.

The atomic mass of an element, which you see on the periodic table, presents the weighted average of all of the masses for all of the isotopes of that element. When you take a sample of any given element, different types of isotopes occur in a certain percentage in nature. So, for example, the atomic weight of hydrogen (one) is based on the fact that scientists have discovered more protium in the world than tritium. Scientists call this the relative abundance of each isotope.

Based on this, we can calculate the average atomic mass for any element, by calculating the weighted average of the masses of the different isotopes.

Review examples of how scientists calculate atomic mass from isotope masses and relative abundances in Problem Example 4 and Problem Example 5, and the "Average Atomic Masses" video in Relative Atomic Masses: The Atomic Weight Scale.

### 2d. Define atomic number and atomic mass and describe how they apply to isotopes

• Define atomic number and atomic mass.
• How do we determine atomic mass using isotopes?

We use the atomic number and atomic mass to describe different atoms. Review 2c above to respond to these questions.

### 2e. Define Avogadro's number and describe the mole quantification of matter

• Define a mole.
• Use Avogadro's number to convert number of atoms to number of moles.
• Why do we need to use moles to quantify matter?
• Use density and molar mass to determine the molar volume of a substance.

Avogadro's number is essentially a counting number for atoms or molecules.

Avogadro's number is: 6.022 x 1023 . Avogadro's number of particles is one mole.

Think about a mole (mol) as if you have a dozen items: 12 eggs and 12 cars. While the size and mass of the eggs and cars differs tremendously, you still have a dozen. In this case, you have a mole (or 6.022 x 1023) of objects or particles (rather than a dozen). Because Avogadro's number is so large we really only use it to describe quantities of atoms and molecules.

Review a brief explanation of Avogadro's number in the orange box at the end of Counting Atoms: Avogadro's Number.

Scientists use a mole, the SI (Systeme Internationale) unit, for chemical entities (Avogadro's number of particles). This commonly-agreed-upon unit of measure allows chemists to easily measure and discuss macroscopic (visible to the naked eye) amounts of atoms or molecules.

We can use Avogadro's number (a conversion factor) to convert among a number of particles (such as atoms) and a number of moles of a given substance.

Review Problem Example 3 in Moles and Their Uses.

The atomic masses listed in the periodic table also correspond to the molar mass of the element using the units, grams per mole (grams/mole or g/mol). For example, carbon has an atomic mass of 12.01 amu (atomic mass unit), and a molar mass of 12.01 g/mol. This correspondence allows us to convert among the macroscopic measurements we make (or the mass in terms of grams) to the microscopic (or the number of atoms) we cannot see. We can perform these conversions using the molar mass of an element and Avogadro's number.

To determine the molar mass of a molecule, simply add up the molar masses for each element in the compound.

Practice converting between grams, moles, and number of particles in Problem Example 4 and Problem Example 5 in Moles and Their Uses.

The molar volume of a substance is the volume one mole of the substance occupies. To determine the molar volume of a substance, you need to use the molar mass and density. Be careful to make sure the units are the same.

Practice calculating molar volume in Problem Examples 6 and 7 in Moles and Their Uses.

### 2f. Discuss the wave-particle duality of light

• Define quantum particle.
• Describe Young's Double Slit experiment.
• How does light both exhibit wave and particle properties?
• How do quantum particles exhibit both wave and particle properties?

The concept of "wave-particle duality of light" is a cornerstone of the field of quantum mechanics.

A quantum particle is a very small particle we can describe as a wave or a particle, depending on how we measure it. For example, under different experimental conditions, we can describe light as a wave or a particle.

Young's Double Slit Experiment identified the wave properties of light and matter.

In this experiment, Thomas Young (1773-1829), a British physician, shined a beam of light through two small slits onto a detector. When the beam of light hit the double slit, it divided into two and then recombined. The light showed an interference pattern or diffraction pattern which can only occur when the light has wave properties.

Albert Einstein (1875-1955), the famous German physicist, inferred the particle nature of light when he worked on the photoelectric effect. In his experiment, he shined a high-energy beam of light onto a metal surface, which caused an electron to eject from the metal. This led him to conceive of the idea of photons, or light particles with distinct energy.

We can describe the energy of a photon of light in mathematical terms as:

$e = hv = \frac{hc}{\lambda}$

(e is the energy of the photon, h is Planck's constant, and v is the frequency of the photon).

Quantum particles also exhibit both wave and particle properties. You can perform the double slit experiment using particles instead of light. If you throw a non-quantum particle (such as a baseball) through the double slit experiment, some particles will go through either slit, which will result in two spots on the detector at each slit.

Note that for this course you do not need to know I wouldn't bother defining it at the general chemistry level. Their text and course materials didn't describe Planck so I think just knowing its a constant in the equation is enough.

However, when a scientist puts a quantum particle through the double slit experiment, the particles will exhibit the same interference pattern Einstein observed for light. This demonstrates that quantum particles exhibit wave properties, in addition to the particle properties we would typically expect.

### 2g. Describe the Bohr model of the hydrogen atom

• What was wrong with the initial planetary model of the atom?
• How did the Bohr model differ from the planetary model of the atom?
• What is meant by quantized energy states?

Niels Bohr (1885–1962), a Dutch physicist, introduced the idea of quantized states of motion for electrons, which became known as the Bohr model of the hydrogen atom. While we now consider this model to be incorrect, it provided an important step in the development of modern atomic theory.

The planetary model of the atom consists of a nucleus containing protons and neutrons, and the electrons spinning around the nucleus, much like planets orbiting the sun. The problem with this model lies with the electrostatics of the electrons in orbit around the nucleus. If the electrons in an atom followed an orbit around the nucleus, they would eventually spiral into the nucleus because they are attracted to the positive protons.

Bohr altered the planetary model of the atom to limit electrons to specific energy states: they would not be able to spiral into the nucleus, based on their angular momentum. He determined electrons would remain in their orbits at specific radii, which he expressed in the following mathematical equation:

$r = \frac{nh}{2 \pi mv}$

(r is the radius of the electron, h is Planck's constant, m is the mass of the electron, v is the orbital velocity of the electron, and n is an integer value. Note that you do not need to know the exact definition for Planck's constant for this course, for this level of chemistry. Just know that it is a constant.)

The value n is known as a quantum number. This quantum number defines where the electron exists, with respect to the nucleus. The larger the quantum number, the further away it is from the nucleus. In other words, the quantum number describes the specific distances where the electrons orbit the nucleus.

It is important to note that electrons can never exist between the n levels. In other words, the electron can be in the n = 1 orbit or the n = 2 orbit, but it can never be in between the two.

You can think about the orbits as energy levels. Energy levels that are further away from the nucleus are higher in energy. This result shows quantized energy states within the atom. Only specific, discrete energy states can exist.

### 2h. List the four quantum numbers and describe their significance

• How does the modern atom model differ from the Bohr atom model?
• List the four quantum numbers and describe what each quantum number tells us about the electron.

We can describe the electrons of an atom in terms of a set of four quantum numbers. These quantum numbers describe the energy and properties of each electron in the atom.

Modern quantum mechanics theory is based on the Schrodinger equation, in which a wave function for each electron describes all quantum mechanical information about that electron. Because electrons are quantum particles, we cannot define their exact location; rather, we can define a probability density region where we are likely to find them.

Bohr's electron orbits were not exactly correct because we cannot precisely define where an electron exists. In the modern model of the atom, we replace orbits with orbitals, or probability density regions where we are likely to find an electron within the atom. This level of uncertainty leads us to our concept of the electron cloud—the region around the nucleus where you are likely to find electrons.

We can describe each electron by a set of four quantum numbers.

The principal quantum number n, describes the distance of the electron from the nucleus. As n increases, the distance from the nucleus increases, and the energy of the electron increases.

You can determine the potential energy of an electron based on its principal quantum number using an equation you can find under the heading "Physical Significance of N" in Section 2 of The Quantum Atom.

The principal quantum number shows the electron "shells" surrounding the nucleus where you are likely to find an electron. We denote the principal quantum number with integer values.

The angular momentum quantum number l, describes the shape of the orbital that the electron is in. We denote the angular momentum quantum number with number and letter designations.

• If l equals zero, we say it is an s orbital and it is spherical.
• If l equals one, we say it is a p orbital and it is dumbbell shaped.
• If l equals two, we say it is a d orbital and it is the shape of "double dumbbells".
• For larger atoms, we also see l equals three orbitals, which are called f orbitals.

The magnetic quantum number m, denotes the orientation within space of the orbital containing the electron.

• For s equals zero, the orbital is spherical shaped. Therefore, it cannot be oriented in different directions in space. However, for the other l values, the orbitals can be oriented in different ways.

The magnetic quantum number can assume 2l + 1 values from negative l (–l) to l.

• For l equals zero (s orbital), m equals one.
• For l equals one (p orbital), m can be negative one, zero, or one.
• For l equals two (d orbital), m can be negative two, negative one, zero, one, or two.

The final quantum number, called the spin quantum number s, is a result of the Pauli Exclusion Principle, which states that no two electrons in an atom can have the same set of quantum numbers. Every orbital can contain two electrons. Therefore, two electrons can have the same n, l, and m quantum numbers. So, to distinguish the two electrons in a given orbital, we have s = +1 and s = –1 for the two electrons in a given orbital.

### 2i. Describe the structure and organization of the periodic table

• Identify the periods and groups on the periodic table.
• Identify the blocks on the periodic table.
• Identify the families on the periodic table.

The periodic table is one of the most important tools that chemists use. Its organization allows us to determine a great deal of information about the elements.

On the periodic table, the rows are called periods. The vertical columns are known as groups. Elements in a group share certain characteristic properties.

Chemists also define blocks on the periodic table, based on the outermost filled electron shell. Review "Section 3: The Aufbau Rules" from Electrons in Atoms.

The blocks are labeled in red in the periodic table:

Chemists have also named families in the periodic table for groups of elements that have similar properties. Many of these names have historical roots. The families labeled in the following chart include: alkali metals, alkaline earths, transition metals, post-transition metals, noble gases, semimetals (metalloids), halogens, lanthanides and actinides.

### Unit 2 Vocabulary

• Angular momentum quantum number
• Atom
• Atomic mass
• Atomic nucleus
• Atomic number (Z)
• Atomic weight
• Bohr Model of the atom
• Diffraction pattern
• Double Slit Experiment
• Electron
• Electron cloud
• Interference pattern
• Ion
• Isotope
• Magnetic quantum number
• Mass number (A)
• Molar mass
• Molar volume
• Mole (mol)
• Neutron
• Orbital
• Pauli exclusion principle
• Periodic table
• Periodic table (group, period, family)
• Photon
• Planetary model
• Planck's constant
• Principal quantum number
• Proton
• Quantum number
• Quantum particle
• Schrodinger equation
• Spin quantum number
• Subatomic particle
• Systeme Internationale (SI)
• Wave-particle duality
• Young's Double Slit Experiment