PCAT: Atomic Structure

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chemistry
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study of the nature and behavior of matter
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atom
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– basic building block of matter – smallest unit of a chemical element – composed of subatomic particles: protons, neutrons, electrons – all atoms of an element show similar chemical properties and cannot be further broken down by chemical means – the mass of the nucleus of an atom comprises almost the entire weight of an atom — but it only occupies 10 ^ -13 of the volume of the atom
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nucleus
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– composed of protons and neutrons – the core of an atom
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orbitals
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the electrons exist outside the nucleus in these characteristic regions of space
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John Dalton’s atomic theory
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– early 1800’s — english scientist — formulate a specific theory of invisible building blocks of matter that are now called atoms — marks the beginning of the modern era of chemistry – key points of hypotheses: 1. all elements are composed of very small particles called atoms — all atoms of a given element are identical in size, mass, and chemical properties (although we now know isotopes, atoms of the same elements with different masses due to different numbers of neutrons, also exist) — the atoms of one element are different from atoms of all other elements 2. all compounds are composed of atoms of more than one element — for any given compound, the ratio of the numbers of atoms of any two of the elements present is either an integer or a simple fraction 3. a given chemical reaction involved only the separation, combination, or rearrangement of atoms; it does NOT result in the creation or destruction of atoms
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protons
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– carry a single positive charge – have a mass of approximately one unified atomic mass unit (amu or u), which is equivalent to one dalton (Da) – carry the same quantity of charge as en electron; however, they have a mass that is approximately 1,840 times greater than that of an electron – symbol: 1 1 H+ — relative mass: 1 — charge: +1 — location: nucleus
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atomic number (Z)
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– equal to the number of protons found in an atom of that element – all atoms of a given element have the same atomic number – indicates the number of electrons in a neutral atom
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neutrons
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– carry no charge – have a mass only slightly larger than that of protons, so it can still be considered to have a mass of approximately 1 u – different isotopes of an element have different numbers of neutrons but the same number of protons – symbol: 1 0 n — relative mass: 1 — charge: 0 — location: nucleus
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electrons
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– carry a charge equal in magnitude but opposite in sign to that of protons – very small mass, approximately 1/1,837 the mass of a proton or neutron – symbol: e- — relative mass: 0 — charge: -1 — location: electron orbitals
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valence electrons
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– the electrons in the electron shell farthest from the nucleus – the farther the valence electrons are from the nucleus, the weaker the attractive force of the positively charged nucleus, and the more likely the valence electron are to be influenced by other atoms
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reactivity of an atom
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– determined by the valence electrons and their activity – in a neutral atom, the number of protons and electrons are equal
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ions
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– a positive or negative charge on an atom is due to a loss or gain of electrons – (+) charge indicates a loss of negative electrons – (-) charge indicates a gain of electrons
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eg. determine each number of protons, neutrons, and electrons in a nickel-58 atom and in a nickel-60 2+ cation
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– 58Ni has an atomic number of 28 and a mass of 58 — therefore, 58Ni has 28 protons, 28 electrons, and 30 neutrons (58-28) – 60Ni2+ still has 28 protons, but since it has a positive charge, it has lost 2 e- — so there are 26 electrons — since the mass number is two units higher, there are 32 neutrons
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atomic mass number (A)
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– equal to the total number of nucleons (protons and neutrons) – the convention A Z X is used to show both the atomic number and the mass number of an X atom where Z is the atomic number, and A is the mass number such that: mass number (A) = # protons + # neutrons
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molecular weight
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– the weight in grams per one mole (mol) of a given element (g/mol)
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mole
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– a unit used to count particles – represented by Avogadro’s number
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Avogadro’s number
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6.02 x 10^23 particles/mol – represents how many atoms of carbon are in 12.0 g of carbon-12 – the conversion factors between amu and g such that it one atom of nitrogen has a mass of 12 u, then one mole of nitrogen has a mass of 14 g
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isotopes
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– same number of protons, different number of neutrons (same Z, different A) – referred by the name of the element, followed by the mass number – eg. carbon-12 (12 6 C) is a carbon atom with 6 protons and neutrons, while carbon-14 (14 6 C) is a carbon atom with 6 protons and 8 neutrons – since isotopes have the same number of protons and electrons, they generally exhibit the same chemical properties
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in nature
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– almost all elements exist as a collection of two or more isotopes — these isotopes are usually present in the same proportions in any sample of naturally occurring element
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standard atomic weight
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– another common convention used to define the mass of an atom – it is a weighted average of all the isotopes of an element found naturally on earth
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periodic table
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– lists the atomic weight for the different elements, which accounts for the relative abundance of the various isotopes – the presence of these isotopes accounts for the fact that the accepted atomic weight for most elements is not a whole number – eg. 14N is much more common (99.6%) than 15N, so the weighted average of the two is 14.007 – eg. element Q consists of three different isotopes: A, B, and C — A has an atomic mass of 40 u and accounts for 60% of naturally occurring Q — B has an atomic mass of 44 u and accounts for 25% of naturally occurring Q — C has an atomic mass of 41 u and accounts for 15% of naturally occurring Q — what is the atomic weight of element Q? * 0.60 (40 u) + 0.25 (44 u) + 0.15 (41 u) = 24 u + 11 u + 6.15 u = 41.15 u = atomic weight of element Q
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Bohr’s model of the hydrogen atom
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– 1911: Ernest Rutherford provided experimental evidence that an atom has a dense, positively charged nucleus that accounts for only a small portion of the volume of the atom – 1900: Max planck developed the first quantum theory, proposing that energy emitted as electromagnetic radiation from matter comes in discrete bundles called quanta — the energy value of a quantum is given by the equation E=hf (where h is a proportionality constant known as Planck’s constant — 6.262 x 10^-34 Js and f [sometimes designated v] is the frequency of the radiation) – 1913: Niels Bohr used the work of Rutherford and Planck to develop his model of the electronic structure of the hydrogen atom
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the Bohr model
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– from Rutherford’s findings, Bohr assumed that the hydrogen atom consisted of a central proton around which an electron traveled in a circular orbit, and that the centripetal force acting on the electron as it revolved around the nucleus was the electrical force between the positively charged proton and the negatively charged electron – Bohr’s model used the quantum theory of Planck in conjunction with concepts from classical physics: in classical mechanics, an object (such as an electron) revolving in a circle may assume an infinite number of values for its radius and velocity – therefore, the angular momentum (L=mvr) and kinetic energy (KE = mv^2) can take on any value – however, by incorporating Planck’s quantum theory into hid model, Bohr placed conditions on the value of the angular momentum – like Planck’s energy, the angular momentum (L) of an electron is quantized according to the following equation: L = nh / 2pi – where h = Planck’s constant — n = principal quantum number (any positive integer) — since h and pi are constant, the angular momentum changes only in discrete amounts with respect to n – Bohr then equated the allowed values of the angular momentum to the energy of the electron obtaining the following equation: E = – Ry / n^2 – where Ry = an experimentally determined constant (Rydberg energy and representing the product of three different constants, RH, h, and c) = 2.18 x 10^-18 J/e- – therefore, like angular momentum, the energy of the electron changes in discrete amounts with respect to n – a value of zero energy was assigned to the state in which the proton and electron were separated completely, meaning that there was no attractive force between them — therefore, the electron in any of its quantized states in the atom would have a negative energy as a result of the attractive forces between the electron and proton — this explains the negative sign in the about equation for energy
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applications of the Bohr model
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– in his model of the structure of hydrogen, Bohr postulated that an electron can exist only in certain fixed-energy states – in terms of quantum theory, the energy of an electron is quantized – using this model, certain generalizations concerning the characteristics of electrons can be made – the energy of the electron is related to its orbital radius (the smaller the radius, the lower the energy state of the electron) – the smallest orbit radius an electron can have corresponds to n = 1, which is the ground state of the hydrogen electron – at the ground state level, the electron is in its lower energy state – the Bohr model is also used to explain the atomic emission spectrum and atomic absorption spectrum of hydrogen, and it is helpful in interpretation of the spectra of other atoms
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atomic emission spectra
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– at room temperature, the majority of atoms in a sample are in the ground state — however, electrons can be excited to higher energy levels by heat energy to yield the excited state of the atom — because the lifetime of the excited state is brief, the electrons will return rapidly to the ground state while emitting energy in the form of photons — the electromagnetic energy of these photons may be determined using the following equation E = hc / lambda – where h = Planck’s constant — c = velocity of light in a vacuum (3.00 x 10^8 m/s) — lambda = wavelength of the radiation – the different electrons in an atom will be excited to different energy levels — when these electrons return to their ground states, each will emit a photon with a wavelength characteristic of the specific transition it undergoes — the quantized energies of light emitted under these conditions do not produce a continuous spectrum (as pelted from classical physics) – rather, the spectrum is composed of light at specific frequencies and is this known as a line spectrum, where each line on the emission spectrum corresponds to a specific electronic transition – because each element can have it electrons excited to different distinct energy levels, each element possesses a unique atomic emission spectrum (which can be used as a fingerprint) – one particular application of atomic emissions spectroscopy is in the analysis of stars’ although physical samples of the stars cannot be taken, the light from a star can be resolved into its component wavelengths, which are then matched to the known line spectra of the elements
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the Bohr model of the hydrogen atom explaining the atomic emission spectrum of hydrogen
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– the simplest emission spectrum among all the elements – Balmer series: the group of hydrogen emission lines corresponding to transitions from upper levels n > 2 to n = 2 (four wavelengths in the visible region) – Lyman series: the groups corresponding to transitions between upper levels n > 1 to n = 1 (higher energy transitions in the UV region)
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Lyman series
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nf: 1 ni: 2, 3, 4… spectrum region: ultraviolet
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Balmer series
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nf: 2 ni: 3, 4, 5… spectrum region: visible and ultraviolet
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Paschen series
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nf: 3 ni: 4, 5, 6… spectrum region: infrared
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when the energy of each frequency of light observed in the emission spectrum of hydrogen was calculated according to Planck’s quantum theory
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– the values obtained closely matched those expected from energy level transitions in the Bohr model – that is, energy associated with a change in the quantum number from an initial ni to a final value nf is equal to the energy of Planck’s emitted photon: E = hc / lambda = -Ry [(1 / ni^2) – (1 / nf^2)] – and the energy of the emitted photon corresponds to the precise difference in energy between the higher-energy initial state and the lower-energy final state
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atomic absorption spectra
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– when an electron is excited to a higher energy level, it must absorb energy – the energy absorbed as an electron jumps from an orbital of low energy to one off higher energy is characteristic of that transition — the excitation of electrons in a particular element results in energy absorption at specific wavelengths – thus, in addition to an emission spectrum, every elements possesses a characteristic absorption spectrum – the wavelengths of absorption correspond directly to the wavelengths of emission since the energy difference between levels remains unchanged – absorption spectra can thus be used in the identification of elements present in a gas phase sampled
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quantum mechanical model of atoms
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– Bohr’s model does not take into consideration the repulsion between multiple electrons surrounding one nucleus – the most important difference between the Bohr model and modern quantum mechanical models is that Bohr’s assumption that electrons follow a circular orbit at a fixed distance from the nucleus is no longer considered valid — rather, electrons are described as being in a state of rapid motion within regions of space around the nucleus called orbitals
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orbital
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a representation of the probability of finding an electron within a given region
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Heisenberg uncertainty principle
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– states that it is impossible to simultaneously determine, with perfect accuracy, the momentum (mass x velocity) and the position of an electron – this means that if the momentum of the electron is being measured accurately, its position will not be certain, and vice versa
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quantum numbers
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– modern atomic theory states that any electron in an atom can be completely described by four quantum numbers: 1. n 2. l 3. ml 4. ms – the value of n limits the values of l, which in turn limit the values of ml – the values of three of the quantum numbers quantitatively give information about the orbitals: 1. n = size 2. l = shape 3. ml = orientation of the orbital
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Pauli exclusion principle
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no two electrons in a given atom can possess the same set of four quantum numbers
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energy state
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the position and energy of an electron described by its quantum numbers
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principal quantum number
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– denoted by the letter n – used in Bohr’s model that can theoretically take on any positive integer value – represent the shell where an electron is present in an atom – the maximum n that can be used to describe the electrons of an element at its ground states corresponds with that element’s period (row) in the periodic table — eg. nitrogen is in period 2 — so neutral N in its ground state has electrons with n values of 1 and 2 — the larger integer value of n, the higher the energy level and radius of the electron’s orbit — the maximum number of electrons in an electron shell n is 2n^2 – the difference in energy between adjacent shells decreases as the distance from the nucleus increases because the difference is related to the expression (1/n2^2) – (1/n1^2) — eg. the energy difference between the third and fourth shells (n= 3 and n=4) is less than that between the second and third shells (n=2 and n=3)
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azimuthal quantum number
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– azimuthal (angular momentum) – denoted by the letter l – tells us the shape of the orbitals and refers to the subshells or sub levels that occur within each principal energy level – for any given n, the value of l can be any integer in the range of 0 to n-1 – the four subshells corresponding to l = 0, 1, 2, 3 are known as the sharp, principal, diffuse, and fundamental subshells or s, p, d, and f subshells, respectively – the maximum number of electrons that can exist within a subshell is given by the equation 4l + 2 – the greater the value of l, the greater the energy of the subshell — however, the energies of subshells from different principal energy levels may overlap — eg. the 4s subshell will have a lower energy than the 3d subshell because its average distance from the nucleus is smaller
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magnetic quantum number
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– denoted ml – described the orientation of the orbital (a specific region within a subshell that may contain no more than 2 electrons) in space – specifies the particular orbital within a subshell where an electron is highly likely to be found at a given point in time – the possible values of ml are all integers from l to -l including 0 – therefore, the s subshell (l = 1) has three possible ml values (-1, 0, +1) and three orbitals – the d subshell (l = 2) have five possible ml values (-3, -2, -1, 0, +1, +2, +3) and contains seven orbitals – the shape and energy of each orbital are dependent upon the subshell in which the orbital is found — eg. a p subshell with its three possible ml values (-1, 0, +1) has three dumbbell-shaped orbital that are oriented in space around the nucleus along the x, y, and z axes — these orbitals are often referred to as px, py, and pz
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spin quantum number
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– denoted by ms – the spin of a particle is its intrinsic angle momentum and is a characteristic of a particle – the two spin orientations are: +1/2 and -1/2 – whenever two electrons are in the sam orbital, they must have opposite spins – electrons in different orbitals (different ml values) with the same ms values are said to have parallel spins – electrons with opposite spins (different ms values) in the same orbital (same ml value) are often referred to as paired
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electron configuration
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– for a given atom or ion, the pattern by which subshells are filled and the number of electrons within each principal level and subshell are designated by an electron configuration – in electron configuration notation: 1. the first number denotes the principal energy level 2. the letter designates the subshell 3. the superscript gives the number of electrons in that subshell – eg. 2p^4 indicates there are 4 electrons in the second subshell (p) of the second principal energy level (n = 2) – note that the third and fourth quantum numbers (ml and ms) are not indicated in the electron configuration but can be determined for a given electron using the rules from earlier
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when writing the electron configuration of an atom
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it is necessary to remember the order in which subshells are filled
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Aufbau principle
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subshells are filled from lowest to highest energy, and each subshell will fill completely before electrons begin to enter the next one
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(n + l) rule
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– used to rank subshells by increasing energy – states that the lower the sum of the first and second quantum numbers, the lower the energy of the subshell – if two subshells possess the same (n + l) value, the subshell with the lower n value has a lower energy and will fill first
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the order in which subshells are filled
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1s –> 2s –> 2p –> 3s –> 3p –> 4s –> 3d –> 4p –> 5s –> 4d –> 5p –> 6s –> 4f –> 5d –> 6p –> 7s –> 5f –> 6d –> 7p eg. which will fill first, the 3d subshell or the 4s subshell? — for 3d, n = 3 and l = 2, so (n + l) = 5 — for 4s, n = 4 and l = 0 , so (n + l) = 4 — therefore, the 4s subshell has a lower energy and will fill first
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to determine which subshells are filled
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– you must know the number of electrons in the atom – in the case of uncharged atoms: the number of electrons equals the atomic number – if the atom is charged: the number of electrons is equal to the atomic number plus the extra electrons if the atom is negative or the atomic number minus the missing electrons if the atom is positive
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in subshells that contain more than one orbital
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– such as the 2p subshell with its three orbitals – the orbitals will fill according to Hund’s rule
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Hund’s rule
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– states that, within a given subshell, orbitals are filled such that there are a maximum number of half-filled orbitals with parallel spins – electrons “prefer” empty orbitals to half-filled ones because a pairing energy must be overcome for two electrons carrying repulsive negative charges to exist in the same orbital
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the presence of paired or unpaired electrons
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– affects the chemical and magnetic properties of an atom of molecule – if the material has unpaired electrons, a magnetic field will align the spins of these electrons and weakly attract the atom to the field — these materials are said to be paramagnetic – materials that have no unpaired electrons and are slightly repelled by a magnetic field are said to be diamagnetic
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valence electrons
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– those electrons that are in its outer energy shell or that re available for chemical bonding – for elements in groups IA and IIA: only the outermost s electrons are valence electrons – for elements in groups IIIA and VIIIA: the outermost s and p electrons in the highest energy shell are valence electrons – for transition elements: the valence electrons are those in the outermost s subshell and in the d subshell of the next-to-outermost energy shell – for the inner transition elements (the lanthanide and actinide series): the valence electrons are those in the s subshell of the outermost energy shell, the d subshell of the next-to-outermost energy shell, and the f subshell of the energy shell two levels below the outermost shell – groups IIIA-VIIA elements beyond period 2 might, accept electrons into their empty d subshells, which gives them more than 8 valence electrons

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