Ch. 3 (Atomic Structure)

Explain electromagnetic radiation, the electromagnetic spectrum, and the speed of light.

• Electromagnetic radiation is so-named because it moves as radiant energy through space with two perpendicular components — an oscillating electric field and an oscilating magnetic field.

• The electromagnetic spectrum includes a multitude of forms of radiation, all varying wavelengths and frequencies.

• The speed of light is 2.998 × 10^8m/s.

Explain wavelength and frequency.

• A wavelength is the distance from one wave crest to the other.

• A frequency is the number of crests that pass a stationary point in space every second.

  • Has the units of waves per second, or Hertz (Hz).

• The two have a reciprocal relationship.

What is the formula for wavelength?

Where “lambda” is wavelength (meters), v is velocity (meters per second), and f is frequency (in Hertz)

What formula relates wave speed, wavelength, and frequency?

Where v = velocity (in meters per second), c is the speed of light in a vacuum (2.998 × 10^8 m/s), and lambda represents wavelength (in meters).

Explain the discovery of the Fraunhofer lines.

Through a glass prism that captured the spectrum of sunlight, Fraunhofer observed a series of very narrow dark lines, and the spectrum wasn’t completely continuous.

Explain the discovery of the atomic emission spectra and what it means.

• Wilhelm Bunsen vaporized elements over a burner and discovered that they emitted spectra that were opposite Fraunhofer’s; that is, they consisted of a dark background with only a few bright-colored lines, and they all had their own patterns of dark lines.

• This meant that at very high temperatures, the atoms of each element emit a characteristic spectrum, and conversely, gaseous elements absorb electromagnetic radiation from external sources.

Explain the atomic absorption spectra.

• When a gaseous element absorbs radiation (in the form of visible light), it has its own unique pattern of dark lines at the same wavelengths as in that element’s emission spectrum.

What are blackbody radiators?

They are sources of radiant energy that emit lower and lower frequencies of radiation the higher their temperatures are.

What was Planck’s theory of energy, the constant named after him, and what was his equation?

• He believed they were emitted as integral multiples of a quantum rather than continuously.

• He created the Planck constant, 6.626 × 10^-34 J . s

• His equation was E = hv, where v is the frequency of the radiation and h is the Planck constant, while E is the energy of the photon.

What equation relates the energy of a quantum of electromagnetic radiation to its wavelength?

Where E is the energy of the photon, h is the planck constant, c is the speed of light, and lambda is the wavelength of the radiation.

Explain photons and their connection to the brightness of an energy source.

• They are tiny packets of radiant energy (e.g. the “building blocks” of electromagnetic radiation), as laid out by Planck’s quantum theory.

• A radiant energy source’s brightness is the sum of the energies of the massive amount of photons produced per unit of time.

Explain the photoelectric effect, the threshold frequency, and a material’s work function.

• The photoelectric effect is a phenomenon in which a material releases electrons after said material absorbs electromagnetic radiation.

• The threshold frequency is the minimum frequency of light required to produce the photoelectric effect in a certain material.

• The work function of a material is the minimum quantity of energy needed for it to emit photoelectrons.

Explain the work function equation.

• ϕ is the minimum amount of energy needed to remove an electron; h is the planck constant and v_o is the threshold frequency.

• The energy that is in excess of the minimum threshold is imparted to each ejected electron as kinetic energy.

What equation is used to calculate the wavelengths of light in nanometers?

• A = 364.56nm(m²/m² - n²)

• Where m is an integer greater than 2, and n is 2.

What equation is used specifically for hydrogen’s spectral lines? Explain why wave numbers are used.

• Where n₁ and n₂ are any positive integers (representing energy levels inside a hydrogen atom) and R_h is the Rydberg constant; the leftmost term is the reciprocal of wavelength, known as the wavenumber.

• Rydberg used the wavenumber because a photon’s energy is inversely proportional to its wavelength, and, as such, a photon’s energy is directly proportional to its wavenumber.

• The difference between n₁ and n₂ is also equal to the energy of a photon that a hydrogen atom absorbs or emits.

What is Rydberg’s constant?

R_h = 1.0974 × 10^7

How are the Balmer equation and Rydberg equation related?

• The Balmer equation represents a special case of Rydberg’s equation, where n₁ = 2.

Explain the Bohr model of atoms and the equation he uses.

• Electrons occupy energy levels (the n constant) and the further away they are from the nucleus, the more energy they carry.

• In a hydrogen atom, electrons have negative energy because its electrostatic potential with the positively-charged nucleus is negative and becomes less negative as there is more distance between it and the positively-charged nucleus.

• E = -2.178 × 10^-18 J (1/n²)

  • Where n = 1, 2, 3. . . up to positive infinity, and the closest electron to the nucleus has the most negative energy.

Explain the equation for the change in energy of an electron.

• Where N_final is its ending energy and N_initial is its starting energy.

• When an electron moves away from the nucleus, delta is positive because it indicates that the electron gained energy.

• By contrast, when it moves towards the nucleus, delta is negative because it indicates that the electron lost energy.

• Ionization takes place when N_final is equal to infinity.

Explain ground states, excited states, and electron transitions.

• An atom in its ground state occupies the lowest-energy state and its electrons are in the lowest energy level.

• An excited state is any energy state above the ground state.

• An electron transition refers to the movement of any electron between two energy levels, where it will move up or down by absorbing a quantum of energy that matches the energy difference between the two states.

Explain the theory of electrons as waves and give the de Broglie equation.

• This is the theory that electrons behave as waves of matter as well as particles of matter, where its wavelength is inversely proportional to its energy.

• The equation by de Broglie allows you to calculate the wavelength of an electron (or any particle) in motion, where m is the particle’s mass, v (or u) is its speed, and h is Planck’s constant.

  • The product of its mass and speed is known as its momentum; the more momentum, the shorter its wavelength.

Explain standing waves and nodes.

• A standing wave is a wave confined to a given space; its wavelength is related to the length L of the space by L = n(lambda/2), where n is a whole number that represents the lowest frequency and longest wavelength possible.

• A node is a location in a standing wave that experiences no displacement; in the context of orbitals, nodes are locations at which electron density goes to zero.

How is the circumference of a circular wave related to its wavelength, and what is the equation for this?

• Standing waves are only produced when the circumference of the circlular wave equals a whole-number multiple of the electron’s wavelength, where the circumference is equal to n * wavelength; otherwise, it is an unstable and discontinuous wave.

• The orbit label n also represents the number of matter-wave wavelengths in that orbit’s circumference.

• Furthermore, the lowest energy possible for an electron occurs for a standing wave with a circumference equal to the wavelength.

Explain the Heisenberg Uncertainty Principle and its characteristic equation.

• The only means of observing an electron clearly would be to use very high-frequency radiation that would end up shifting it off-course; thus, we can simultaneously know both an electron’s position and its momentum (product of its mass * its speed).

• This is expressed as the given equation, where delta x is the uncertainty in the electron’s position, m is its mass, delta u is the uncertainty in its speed, and h is the planck constant.

• This uncertainty is the foundation of the quantum theory.

What is the quantum mechanics and its characteristic set of equations?

• Also known as wave mechanics, these are the mathematical foundation of electrons as waves.

• Its characteristic set of equations invented by Schrodinger are known as the Schrodinger wave equation, where solutions to it are known as wave functions; these describe how the matter wave of an electron in an atom varies in both time and location.

Explain Schrodinger’s model of wave functions, his wave equations, and how physicist Max Born dissented.

• Schrodinger created a wave equation, whose solutions are called wave functions, that mathematically describe how an electron’s matter wave varies in time and location within the atom; wave functions define the energy levels in the hydrogen atom.

• He believed wave functions depicted an electron’s “smearing” through 3D space, but Max Born dissented and proposed that the square of a wave function indicates the probability of finding an electron within an atom.

Explain Schrodinger’s wave equation and orbitals.

• As previously stated, Schrodinger’s wave equation describes how an electron’s matter wave varies in time and location in an atom, while their solutions (wave functions) depict energy levels in the hydrogen atom.

• Orbitals refer to any region of space in an atom in which there is a high probability of finding an electron; these are 3D volumes of space with distinctive shapes, orientations, and distances from the nucleus, each one being a solution to Schrodinger’s wave equation.

Explain quantum numbers.

• In Schrodinger’s equation, each orbital is a solution, and each is identified by a unique combination of three integers called quantum numbers.

• The principal quantum number is like Bohr’s n value for the hydrogen atom in that it’s a positive integer that indicates the relative size and energy of an orbital or of a group of orbitals in an atom.

  • A larger value of n generally reflects increasing energy levels and distance from the nucleus.

• The angular momentum quantum number is an integer with a value ranging from zero to (n - 1). This defines the shape of an orbital.

• The magnetic quantum number is an integer with a value from all integers between -l and +l, defining the orientation of an orbital in the space around an atom’s nucleus.

Explain the relationships within the quantum numbering system.

• The nth shell has n subshells and n² orbitals.

• Each subshell has 2l + 1 orbitals.

Explain the concept of electron spin and the spin quantum number.

• Pairs of lines called doublets in atomic emission spectra are caused by a propertty called electron spin, where electrons spin in one or two directions, either up or down.

• A moving electron creates a magnetic field by moving through space, and the spinning motion produces a second magnetic field either oriented up or down, designated a fourth quantum number known as the spin quantum number, which can be ½ (spin up) or -1/2 (spin down).

Explain how electron presence relates to the orbital it is in, as well as the term for this concept.

• The closer an orbital is to the nucleus, the lower the probability of finding an electron around it, since the radius is very small; on the other hand, the further you get from the nucleus, the higher the probability - until you eventually reach a threshold where electron density probability begins to diminish again due to distance from the nucleus.

• This is also known as a radial distribution profile.

Explain the aufbau principle and how it relates to chemical reactivity.

• The afbau principle states that the electrons are placed in the lowest-energy orbitals available and that each orbital can have no more than two electrons (on the basis of Pauli’s exclusion principle).

• The core electrons (innermost electrons) are uninvolved in chemical reactions.

Explain the concept of effective nuclear charge and why earlier subshells are filled first.

• Between, for instance, a 2s and 2p orbital and the nucleus, there will be electrons in the 1s orbital whose negative charges shield the 2s and 2p orbital electrons from the nucleus’s positive charge; it is said that the 2s and 2p orbital electrons experience an effective nuclear charge that is less than that exhibited by the nucleus.

• The subshells that come earlier are filled first because they are more strongly attracted to the nucleus. Starting with period 4, the outermost s orbitals fill before (n - 1)d orbitals do.

Explain Hund’s rule and the rule of ionization.

• It is the principle that when electrons fill orbitals of equal energy, it will occupy them firstly with parallel spins before they begin to pair up.

• The rule of ionization is that typically, valence shells are ionized before anything else to pry apart; electrons with the highest n value are always ionized first, even though they will not necessarily be the furthest ones away from the nucleus.

Explain ionization trends across the transition metals and explain some of the reasons for deviant electron configurations.

• Because they preferentially lose electrons from their outer shells first, many of them forms 2⁺ charges. Some also form 1⁺ charges because they only have one electron to lose.

• Sometimes, half-filled shells will be more stable than full-filled shells (due to less electron-to-electron repulsion), hence the deviant phenomena of some transition metals “skipping” certain sublevels after a certain number of electrons within them.

Explain how atomic sizes are expressed.

• They are measured in terms of their radii, and radii is taken from between atoms to determine a certain atom’s exact radius (since the wavelike phenomenon of electrons renders atoms’ edges undefinable)

• The radius of a metal is half he distance between the nuclear centers in the solid metal, and ionic radii are derived from half thedistance between nuclear centers in solid ionic compounds.

Explain the trend of atomic sizes across the periodic table; explain why they are the way they are, particularly for groups.

• From top to bottom across periods, atomic sizes increase.

• From left to right across groups, atomic sizes decrease, despite their increasing atomic number.

• The two competing interactions that dictate atomic size are. . .

  • Increasing effective nuclear charge between protons and shelled electrons; this is why atomic sizes decrease across a group.

  • Increasing repulsion between valence electrons; in theory, this should make atomic sizes larger across a group, but the increasing effective nuclear charge more than offsets this.

Explain trends in ionic size.

• Cations of the main group elements are much smaller than their parent atoms, but anions are much larger.

• Two isoelectronic atoms may have different sizes due to varying nuclear charges.

Explain ionization energy and how it relates to atomic emission spectra.

• Ionization energy is the energy needed to remove 1 mole of electrons from 1 mole of gas-phase atoms or ions in their ground state.

• It is part of the experimental evidence that supports energy levels in electron configurations.

Explain the different types of ionization energies.

• The ionization energy to remove a mole of electrons from a mole of atoms to make a mole of 1+ cations is called the first ionization energy.

• The ionization energy to remove a moleof electrons from a mole of 1+ cationst to make a mole of 2+ cations is the second ionization energy.

• And so on, and so forth . . .

Explain the trend in ionization energies across the periodic table and the exceptions.

• Increasing effective nuclear energy will increase the strengths of attractive forces between nuclei and valence electrons, which, in turn, increases its ionization energy.

• Typically, first ionization energies increase from left to right across a period and decrease from top to bottom across a group.

  • There is one anomaly between the group 2 and group 13 elements that are next to each other in the second and third rows; a decrease in IE₁ occurs between Be and B, and between Mg and Al; B and Al lose a p electron upon ionization, whereas Be and Mg lose an s electron.

  • The second anomaly is between group 15 and group 16; an electron lost in a group 15 element was originally alone and unpaired, but a lost electron in group 16 would have been previously paired, which means less stability and, therefore, less ionization energy required.

Explain photoelectron spectroscopy and how it is another piece of experimental evidence.

• While ionization energy provides evidence for the existence of core vs valence electrons, they do not give insight into energy differences between electron within the same shell.

• Photoelectron spectroscopy does this by experiementally determining kinetic energies of irradiated, ejected electrons, and subsequently using them to calculate those electrons’ binding energies; these are converted into photoelectron spectrum graphs.

Explain electron affinities.

• These are the changes in energies when electrons are added to form monoatomic anions, when one mole of electrons is added to one mole of atoms or ions in the gas phase.

• This number is typically negative since it indicates that energy was lost (or released), because adding an electron tends to produce a more stable ion than the free atom and electron pre-convergence.

Explain the patterns of electron affinities (EA).

• They generally increase with increasing atomic number among group 1 and group 17 elements, but other groups do not display a clear trend.

• In general, it becomes more negative with increasing atomic numbers across a period, but there are exceptions.

  • In the group 17 halogens, their high effective nuclear charges give them the most negative EA values since giving them an electron will give them the stable configurations of the noble gases.

  • On the other hand, forming an anion with a group 18 atom will require adding energy because because their high effective nuclear charge.