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Chemistry Chapter 7
A Quantum Model of Atoms, Periodic Properties
| Question | Answer |
|---|---|
| Fraunhofer lines (Atomic Emission/Absorption Spectra) (7.1) | The use of prisms to display a continuous spectrum of visible light (red-violet) revealed a discovery about the sun’s rainbow of colors: it was not continuous. Rather, it contained dark, narrow lines. Furthermore, the Fraunhofer D line corresponded to the yellow-orange light produced by hot sodium vapor (Figure 7.3). On the surface of the Sun, gaseous atoms may absorb particular colors of light, producing an atomic absorption spectrum, which consists of dark lines in an otherwise continuous spectrum. |
| Electromagnetic Spectrum (7.2) | A continuous range of radiant energy that extends from high-energy gamma rays to low-energy radio waves. All forms of radiant energy are examples of electromagnetic radiation. A wave of EM radiation has a characteristic wavelength (λ) and frequency (v). The SI unit for frequency is (Hz), which are also called cycles per second (cps): 1 Hz = 1 cps = 1/s. The product of the wavelength and frequency of any electromagnetic radiation is the universal constant (c) or the speed of light. (2.998 x 10⁸ m/s) |
| c = λv (7.2) | Equation for finding the speed of light. Wavelength and frequency have a reciprocal relationship; as one decreases the other must increase. |
| Amplitude (7.2) | The maximum amount of displacement of a particle on the medium from its rest position. In a sense, the amplitude is the distance from rest to crest. Similarly, the amplitude can be measured from the rest position to the trough position. For example, when looking at a sound wave, the amplitude will measure the loudness of the sound. The energy of the wave also varies in direct proportion to the amplitude of the wave. |
| Nanometer Conversion Factor (7.2) | There are 1 x 10⁹ meters in 1 nanometer. To convert from nanometers to meters, divide your figure by 1,000,000,000. |
| Blackbody Radiation (7.3) | A blackbody is a theoretical or model body which absorbs all radiation falling on it, reflecting or transmitting none. ( |
| E = hv (7.3) | Planck proposed: radiant objects emit energy only in integral multiples of an elementary unit, or quantum, of energy defined by this equation; where (ν) is the frequency of the radiation that such an object emits and (h) is the Planck constant. (6.626 ✕ 10−34 J · s) |
| Quantize(d) (7.3) | Restrict the number of possible values of (a quantity) or states of (a system) so that certain variables can assume only certain discrete magnitude; to subdivide, constraining an input from a continuous or otherwise large set of values to a discrete set (such as the integers, whole numbers of a specific base set). |
| E = hc / λ (7.3) | An equation that relates the energy of a quantum of radiant energy to its wavelength. E represents the number of joules in a single quantum of energy. |
| Photons (7.3) | Tiny packets of radiant energy. A particle representing a quantum of light or other electromagnetic radiation. A photon carries energy proportional to radiation frequency but has zero rest mass (meaning they always move at the speed of light in vacuum). |
| Quantum Theory (7.3) | The observed brightness of a source of radiant energy is the sum of the energies of the enormous number of photons it produces per unit of time. Because Planck’s energy model is characterized by quantum building blocks, it has become known as Quantum Theory. |
| Photoelectric Effect (7.3) | Phenomenon in which electrically charged particles are released from or within a material when it absorbs electromagnetic radiation. Electrons emitted in this manner are called photoelectrons. |
| Threshold Frequency Φ= hv₀ (7.3) | Defined as a minimum frequency under which the photoelectric emission is not possible, regardless of the incident radiation intensity. Here, v₀ is the photoelectric threshold frequency of the electromagnetic light rays, and Φ is the work function of the metal body. |
| Work Function (Φ) (7.3) | This minimum amount of energy is related to the strength of the attraction between the nuclei of surface atoms and the electrons surrounding them. Denoted as Φ. Φ = hv₀ If photoelectric material is illuminated with radiation emitting frequencies higher than (v₀), then any energy excess of (Φ) is imparted as kinetic energy onto the expelled electrons. The higher the frequency of incident light above (Φ), the higher the velocity of e⁻ escaping. |
| Wave-Particle Duality (7.3) | The concept in quantum mechanics that every particle or quantum entity may be described as either a particle or a wave. It expresses the inability of the classical concepts "particle" or "wave" to fully describe the behavior of quantum-scale objects. Possession by physical entities (such as light and electrons) of both wavelike and particle-like characteristics |
| Rydberg Equation (7.4) | A formula used to predict the wavelength of light resulting from an electron moving between energy levels of an atom. Wave Number (1/λ): number of wavelengths/unit of distance. Rydberg Constant: 1.097x 107 m⁻¹ A series of hydrogen emission lines exist in regions outside the visible range, lines with (λ) calculated by replacing n = 2 with n = 1, 3, 4, etc. Discrete frequencies of hydrogen’s emission lines indicated that only certain levels of internal energy were available in hydrogen atoms. |
| Bohr Hydrogen Model [Only applies to atoms/ions with a single (e⁻) in orbit] (7.4) | Bohr proposed a model for the hydrogen atom that assumed its one electron travels around the nucleus in one of an array of concentric orbits. Each orbit represents an allowed energy level and is designated by the value of n. Based on three postulates: 1. an e⁻ moves around the nucleus in a circular orbit 2. e⁻ angular momentum in the orbit is quantized 3. change in an electron’s energy as it makes a quantum jump from one orbit to another is always accompanied by the emission/absorption of a photon |
| Ground State & Electron Transition (7.4) | When an electron is at its lowest energy level it is at its ground state (lower potential energy than an excited state). It may enter an excited state if it absorbs energy that exactly matches the energy difference between the two states. This process works in reverse, electrons may emit energy equal to the difference in E between states, and thus move down energy levels into a less excited/ground state. This absorption/emission is called electron transition. |
| De Broglie Wavelengths/Equation λ = h/mv (7.5) | Where (λ) is wavelength, (h) is Planck's constant, (m) is the mass of a particle, moving at a velocity (v). De Broglie calculated e⁻ wavelengths from Einstein’s equations relating energy and mass, (E = mc²), and the energy and wavelength of a photon, (E = hc/λ). Any moving particle displays wavelike properties. Explained the stability of the e⁻ levels in Bohr’s model by proposing that the e⁻ in an H atom behaves like a circular wave oscillating around the nucleus. |
| Standing Wave (7.5) | Also known as a stationary wave, is a wave that oscillates in time but whose peak amplitude profile does not move in space. Points with zero displacement (two ends of a string) are called Nodes. Electron orbital waves are dictated by (Circumference = nλ) which explains why electrons don't spiral into the nucleus of an atom. (n = 1) is the minimum circumference of an orbiting electron. |
| Heisenberg's Uncertainty Principle (7.5) | To illuminate an e⁻ microscope, we would have to use (γ), or gamma rays. (γ) have high (v) and (E); they would knock e⁻ off course. The only way to illuminate them would be with longer λs, but they'd be too long to match the size of (e⁻). The only means for clearly observing an e⁻ make it impossible to know its motion or its momentum, which is defined as an object’s velocity times its mass. Therefore, we can never know exactly both the position and the momentum of the electron simultaneously. |
| Heisenberg's Uncertainty Equation (7.5) | ΔxΔp ≥ h/(4π) This equation limits us to only knowing the probability of finding an e⁻ at a certain location; they must not move in circular orbitals. Δx = Uncertainty in position Δp = Uncertainty of momentum h = Planck's constant π = Pi Solving this equation for (Δx) provides a measure of the uncertainty of an electron's position within the atom's radius. Solving for (Δp) gives a measure of its uncertain momentum. [Written as: Δxₑ = 5.29 x 10⁻¹¹m] |
| Schrödinger wave equation (7.6) | A mathematical description of electron waves. Solutions to this equation are called (ψ) wave functions; mathematical expressions that describe how the matter wave of an electron in an atom varies both with time and with the location of the electron in the atom. ψ² defines an orbital. It can also be used to calculate the probability of a transition between two orbitals. |
| Orbitals (7.6) | Three-dimensional regions of space with distinctive shapes, orientations, and average distances from the nucleus. Each orbital is a solution to Schrödinger’s wave equation and is identified by a unique combination of three integers, or quantum numbers, whose values flow directly from the mathematical solutions to the wave equation. The quantum numbers are: (n, l, m₁, and mₛ). Orbital size increases with increasing values of the principal quantum number (n). |
| Quantum Number (n) (7.6) | An allowed energy level, orbitals with the same n# are in the same shell. Energy levels are fixed distances from the nucleus of an atom. Values of n are whole numbers. At (n = 1), an e⁻ is closest to the nucleus, while (n = 2) the e⁻ would be farther. The principal quantum # corresponds to the row number for an atom on the periodic table. When used in Rydberg equation: n(Final) < n(Initial); the sign of ΔE is negative and the e⁻ has lost energy. Moving away from the nucleus = GAINING energy. |
| Quantum Number (l) (7.6) | The Angular Momentum Quantum Number. An integer with a value ranging from zero to (n − 1) that defines the shape of an orbital. In the past, scientists described line spectra as sharp, principal, diffuse, and fundamental. Hence the use of (s, p, d, f). Orbitals with the same value of (n) and (l) are in the same subshell and represent equal energy levels. Periodic table is divided into blocks characterized by angular momentum numbers. (ex. p-block, s-block, d-block). 1 = s 2 = p 3 = d 4 = f |
| Quantum Number (m₁) (7.6) | Describes the orbital orientation in space. Electrons can be situated in one of three planes in three dimensional space around a given nucleus (x, y, and z). For a given value of the angular momentum quantum number (l), there can be (2l + 1) values for m₁. If (l = 3) then (m₁) can be: -3, -2, -1, 0, 1, 2, 3. |
| Quantum Number (mₛ) (7.6) | The Spin Magnetic Quantum Number. A moving electron (or any charged particle) creates a magnetic field by its motion. The spinning motion produces a second magnetic field oriented up or down. (mₛ) can either be +½ (up) or -½ (down). |
| Pauli's Exclusion Principle (7.6) | Two or more identical fermions (particles with half-integer spin) cannot occupy the same quantum state within a quantum system simultaneously. More specifically, no two electrons in a multi-electron atom can have the same four quantum numbers. Therefore, each orbital can hold TWO electrons (one with upward spin and one with downward spin). |
| Laser Acronym (7.6) | Light Amplification by Stimulated Emission of Radiation. "Stimulated Emission" relates to the fact that atoms in lasers remain in excited states for unusually long times. One incident photon is rapidly amplified into an intense pulse of monochromatic light via the repopulation of an excited state. |
| S-Orbitals (7.7) | Electrons in s-orbitals (even s orbitals with high values of n) have some probability of being close to the nucleus. Nevertheless, 3s electrons are more likely to be farther away from the nucleus than 2s electrons, which are more likely to be farther away than 1s electrons. |
| P-Orbitals (7.7) | All shells with n ≥ 2 have a subshell containing three p-orbitals. Each of these orbitals has three teardrop shaped lobes, oriented across from one another (along each of the three Cartesian axes). These orbitals are named px, py, and pz. An electron in a p-orbital occupies BOTH lobes. |
| D-Orbitals (7.7) | Four of them consist of four teardrop shaped lobes oriented like a four leaf clover. The fifth is different but mathematically equivalent. In three of these orbitals, the lobes are not situated along the x, y, and z axes, but rather in the quadrants formed by the axes. These orbitals are designated dxy, dxz, and dyz. The fourth orbital, called dₓ₂₋ᵧ₂, the lobes lie upon the x/y axes. The fifth, called dᶻ₂, has two lobes on the z axis and a donut shaped torus (y & x axes) surrounding the origin. |
| Aufbau Principle (7.8) | Meaning "to build up" this principle suggests that the most stable atomic structures have the lowest energy orbitals filled before all others. Each electron should be placed in the lowest energy orbital available, and each orbital can house two electrons (with opposite spin numbers). Ground State Configurations: (1) minimizes the total energy of the electrons (2) obeys the Pauli exclusion principle (3) obeys Hund's rule of maximum multiplicity (4) considers the exchange interaction |
| Electron Configuration Notation (7.8) | [For example: 1s¹] Leftmost number is the Principal Quantum Number (n). Letter (s, p, d, f) indicates the type of orbital. Superscript number is the amount of e⁻ within the subshell. In Orbital Diagrams, arrows pointing up indicate a positive spin. Arrows pointing down represent negative spin. A singular box with both (↑↓) is considered to house spin-paired electrons. |
| Filled Shell, Group 18 Condensed Electron Configurations (7.8) | Atoms with filled (s) and (p) subshells are generally chemically stable and inert. All noble gases display this trait (group 18). Condensed configurations can be written by placing the most recent noble gas into a box before adding the valence subshells. This replaces the configurations of the core electrons for the sake of convenience and clarity. (ex. 1s²2s² → [He]2s² for Z=4). |
| Effective Nuclear Charge (Zₑff) [Same charges repel one another] (7.8) | Shielding effect of e⁻ prevents higher orbitals from experiencing the full charge of the nucleus due to the repelling effect of inner layer. An e⁻ in a 2s/2p orbital is attracted to the nucleus, but that e⁻ is partially shielded from the nucleus by the two negative charges on the 1s [↑↓]. Closer proximity means that a 2s e⁻ has a greater Zₑff than an e⁻ in a 2p orbital, even though both are shielded by the 1s [↑↓]. A 2s e⁻ is lower in energy than a 2p e⁻ which makes the 2s orbital fills first. |
| Degenerate Orbitals (7.8) | Designating the 2p orbital as (px), (py), or (pz) is not important because these three orbitals all have the same energy. Electrons do not pair in degenerate orbitals until each orbital is occupied by a single electron. |
| Hund's Rule (7.8) | The lowest-energy e⁻ config. for degenerate orbitals is the one with the max #of unpaired parallel valence e⁻ All e⁻ have a negative charge and repel one another. They occupy orbitals that are as far away from each other as possible, which means the two 2p e⁻ in [C] occupy separate 2p orbitals. Ex: [↑ ] [↑ ] instead of [↑↓] [ ]. Electrons can also fill out of order, as long as they are not occupying the same orbital when there is another empty. For example: [↑ ] [↑ ] [__] = [↑ ] [__] [↑ ]. |
| Excited State (7.8) | The lowest-energy (or first) excited state of sodium is one in which its 3s e⁻ has moved up to a 3p orbital. This excited state has the e⁻ configuration [Ne]3p¹. The e⁻ takes less than a nanosecond to fall back to the ground state. This transition releases a quantum of energy (hν) equal to the difference in energy between the 3p and 3s orbitals in an [Na] atom—the energy of a photon of yellow-orange light. |
| Energy Flow Between Subshells (7.8) | [1s → 2s → 2p → 3s → 3p → 4s → 3d → 4p → 5s → 4d → 5p →6s → 4f → 5d → 6p → 7s → 5f → 6d → 7p → 6f → 7d → 7f] The (n) value of the d-orbitals being filled in a row is always one less than the row number, and the (n) value of the f-orbitals being filled is two less than the row number. When writing configurations, sort by the (n) level. For example, when writing the condensed configuration of [Ga]: [Ar]3d¹⁰4s²4p¹ instead of [Ar]4s²3d¹⁰4p¹ Even though 4s<3d regarding energy level. |
| Electron Configuration of Ions (7.9) | Begin with the e⁻ config. of its neutral parent atom. For a Cation, remove e⁻ from the highest principal quantum number. For Anions, add e⁻ to the next subshells. [Ne]3s¹ → [Ne] + e⁻ (Sodium loses an e⁻). [Na⁺] [F⁻] and [Ne] are all isoelectronic. Many transition metals form ions with 2⁺ charges by losing both electrons from the s-orbital in the outermost shell. E⁻ with the HIGHEST (n) value ionize first (4s > 3d). Sometimes, d-orbital e⁻ are ripped away at the same time, forming 3⁺ or 4⁺ charges. |
| Lanthanides & Actinides (7.9) | Lanthanides have partly filled 4f-orbitals, and actinides have partly filled 5f-orbitals. |
| Pairing Energy (7.9) | The energy required to accommodate two electrons in one orbital. When the pairing energy is high compared with the CFSE (crystal field stabilization energy), the lowest-energy electron configuration is achieved with as many electrons as possible in different orbitals. The additional e⁻ in [Gd] goes to a 5d-orbital instead of a 4f-orbital, which would result in the e⁻ configuration [Xe]4f⁸6s²: A half-filled set of f orbitals is more stable because adding another f electron requires pairing energy. |
| Diamagnetic (7.9) | Being diamagnetic means having all electrons paired and the individual magnetic effects cancel each other out. Paramagnetic and diamagnetic configurations result from the amount of d-electrons in a particular atom. The energy associated with the spin pairing of these configurations relies on a factor of three things, the atom (for its electronic configuration and number of d-electrons), the Crystal Field Theory (field splitting of electrons), and the type of ligand field complex (tetrahedral or octahedral). |
| Paramagnetic (7.9) | Having unpaired e⁻ meaning individual magnetic effects do not cancel one another out. The unpaired e⁻ carry a magnetic moment that is stronger with the # of unpaired e⁻ causing the atom/ion to be attracted to an external magnetic field. When an e⁻ can singly occupy a given orbital, in a paramagnetic state, that config. results in high spin energy. When two e⁻ are forced to occupy the same orbital, they experience a interelectronic repulsion effect which in turn increases the total energy of the orbital. |
| Atomic Radii (7.10) | Metallic radii: half the distance between the nuclear centers in the solid metal. Ionic radii: derived from the distances between nuclear centers in solid ionic compounds. Radius of an element that occurs in nature as a diatomic molecule, such as N₂ and O₂, is half the distance between the nuclear centers in the molecule |
| Trends in Atomic/Ionic Size (7.10) | The distance from the nucleus to the s-orbitals increases as the principal quantum number (n) increases. The atomic radii of elements in the same group of the periodic table increase with increasing atomic number. |
| Increasing Effective Nuclear Charge (7.10) | When the atomic number increases, so does the positive charge of the atom. Therefore, when (Zₑff) increases the size of the atom decreases. More electrons means more electron-electron repulsion, which tends to increase the size of an atom. Cations are much smaller than their main group parents, and anions are much larger. All monatomic anions are larger than the atoms from which they form. |
| Ionization Energy (7.11) | The energy needed to remove 1 mole of electrons from 1 mole of gas-phase atoms or ions in their ground state. Removing these electrons always requires an addition of energy to the system because a negatively charged electron is attracted to a positively charged nucleus, and overcoming that attractive force requires energy. Successive removal takes an increased amount of energy because, for example, an e⁻ must be removed from a 2⁺ ion. |
| First/Second/Etc. Ionization Energy (7.11) | Amount of energy needed to remove 1 mole of electrons from 1 mole of atoms to make 1 mole of cations with a 1⁺ charge is called the First Ionization Energy (IE₁). To make a 2⁺ charge, Second Ionization Energy (IE₂) is required. The easiest element to ionize is the group one element in each row, and the hardest is the group eighteen element (noble gases). The higher the (n) value of a row, GENERALLY the lower the ionization energy needed. |
| Electron Affinity (EA) (7.12) | The change in energy when 1 mole of electrons is added to 1 mole of gas-phase atoms or monatomic cations. In general, electron affinity becomes more negative with increasing atomic number across a row, but there are exceptions to that trend. EA values of main group elements are expressed in kJ/mol. The more negative the value, the more energy is released when 1 mole of atoms combines with 1 mole of electrons to form 1 mole of anions with a 1⁻ charge. When EA is positive (group 18) energy is consumed. |
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