Atomic Structure and Periodic Trends (2)
Ions
When a neutral atom gains or loses electrons, it becomes charged, and the resulting atom is called an ion. For each electron it gains, an atom acquires a charge of -1 unit, and for each electron it loses, an atom acquires a charge of +1 unit. A negatively charged ion is called an anion, while a positively charged ion is called a cation. We designate how many electrons an atom has gained or lost by placing this number as a superscript after the chemical symbol for the element. For example, if a lithium atom loses 1 electron, it becomes the lithium cation Li1+, or simply Li+. If a phosphorus atom gains 3 electrons, it becomes the phosphorus anion P3-, or phosphide.
The Quantum model of the atom
While one-electron atoms produce easily predicted atomic spectra, the Bohr model does not do a good job of predicting the atomic spectra of many-electron atoms. This shows that the Bohr model cannot describe the electron-electron interactions that exist in many-electron atoms. The quantum model of the atom was developed to account for these differences. Bohr's model suggested, and we still hold to be true, that electrons held by an atom can exist only at discrete energy levels- that is, electron energy levels are quantized. This quantization is described by a unique "address" for each electron, consisting of four quantum numbers designating the shell, subshell, orbital, and spin. While the details of quantum numbers are beyond the scope of the MCAT, it is still useful to understand the conceptual basis of the quantum model.
Example: 4-12 Iodinated oleic acid, containing radioactive iodine-131, is administered orally to study a patient's pancreatic function. If 131I has a half-life of 8 days, how long after the procedure will the amount of 131I remaining in the patient's body be reduced to 1/5 its initial value? A) 19 days B) 32 days C) 40 days D) 256 days
Although the fraction 1/5 is not a whole-number power of 1/2, we do know that it's between 1/4 and 1/8. If 1/4 of the sample were left, we'd know that 2 half-lives had elapsed, and if 1/8 of the sample were left, we'd know that 3 half-lives had elapsed. Therefore, because 1/5 is between 1/4 and 1/8, we know that the amount of time will be between 2 and 3 halflives. Since each half-life is 8 days, this amount of time will be between 2(8) = 16 days and 3(8) = 24 days. Of the choices given, only choice A is in this range.
Diamagnetic and Paramagnetic Atoms
An atom that has all of its electrons spin-paired is referred to as diamagnetic. For example, helium, bery|lium, and neon are diamagnetic. A diamagnetic atom must contain an even number of electrons and have all of its occupied subshells filled. Since all the electrons in a diamagnetic atom are spin-paired, the individual magnetic fields that they create cancel, leaving no net magnetic field. Such an atom will be repelled by an externally produced magnetic field.
Excited State vs. Ground State
Assigning electron configurations as we've just discussed is aimed at constructing the most probable location of electrons, following the Aufbau principle. These configurations are the most probable because they are the lowest in energy, or as they are often termed, the ground state. Any electron configuration of an atom that is not as we would assign it, provided it doesn't break any physical rules (no more than 2e- per orbital, no assigning non existent shells such as 2d, etc....) is an excited state. The atom has absorbed energy, so the electrons now inhabit states we wouldn't predict as the most probable ones.
What is half-life?
Different radioactive nuclei decay at different rates. The half-life, which is denoted by t1/2, of a radioactive substance is the time it takes for one-half of some sample of the substance to decay. Thus, the shorter the half-life, the faster the decay. The amount of a radioactive substance decreases exponentially with time, as illustrated in the following graph.
The Orbital Orientation
Each subshell contains one or more orbitals of the same energy (also called degenerate orbitals), and these orbitals have different three-dimensional orientations in space. The number of orientations increases by two in each successive subshell. For example, the s subshell contains one orientation and the p subshell contains three orientations. You should be able to recognize the shapes of the orbitals in the s and p subshells. Each s subshell has just one spherically symmetrical orbital. Each p subshell has three orbitals, each depicted as a dumbbell, with different spatial orientations.
Atomic weight
Elements exist naturally as a collection of their isotopes. The atomic weight of an element is a weighted average of the masses of its naturally occurring isotopes. For example, boron has two naturally occurring isotopes: boron-10, with an atomic mass of 10.013 amu, and boron-11, with an atomic mass of 11.009 amu. Since boron-10 accounts for 20 percent of all naturally occurring boron, and boron-11 accounts for the other 80 percent, the atomic weight of boron is (20%) (10.013 amu) + (80% (11.009 amu) = 10.810 amu and this is the value listed in the periodic table. (Recall that the atomic mass unit is defined so that the most abundant isotope of carbon, carbon-12, has a mass of precisely 12 amu.)
The Electron Spin
Every electron has two possible spin states, which can be considered the electron's intrinsic magnetism. Because of this every orbital can accommodate a maximum of two electrons, one spin-up and one spin-down. If an orbital is full, we say that the electrons it holds are "spin-paired."
Nuclear binding energy
Every nucleus that contains protons and neutrons has a nuclear binding energy. This is the energy that was released when the individual nucleons (protons and neutrons) were bound together by the strong force to form the nucleus. It's also equal to the energy that would be required to break up the intact nucleus into its individual nucleons. The greater the binding energy per nucleon, the more stable the nucleus. When nucleons bind together to form a nucleus, some mass is converted to energy, so the mass of the combined nucleus is less than the sum of the masses of all its nucleons individually. The difference, Δm, is called the mass defect, and its energy equivalent is the nuclear binding energy. For a stable nucleus, the mass defect, Δm = (total mass of separate nucleons) - (mass of nucleus) will always be positive.
Which of these modes of radioactive decay causes a change in the mass number of the parent nucleus? A) α B) β- C) β+ D) γ
Gamma decay causes no changes in the number of protons or neutrons, so we can eliminate choice D. Beta decay (β-, β+, and EC) changes both N and Z by 1, but always such that the change in the sum N+ Z (which is the mass number, A) is zero. Therefore, we can eliminate choices B and C. The answer is A.
Isotopes
If two atoms of the same element differ in their numbers of neutrons, then they are called isotopes. The atoms shown below are two different isotopes of the element beryllium. The atom on the left has 4 protons and 3 neutrons, so its mass number is 7; it's 7Be (or beryllium-7). The atom on the right has 4 protons and 5 neutrons, so it's 9Be (beryllium-9). (These figures are definitely not to scale. If they were, each dashed circle showing the "outer edge" of the atom would literally be about 1500 m- almost a mile across! The nucleus occupies only the tiniest fraction of an atom's volume, which is mostly empty space.) Notice that these atoms--like all isotopes of a given element--have the same atomic number but different mass numbers.
The Energy Subshell
In the quantum model of the atom, however, we no longer describe the path of electrons around the nucleus as circular orbits, but focus on the probability of finding an electron somewhere in the atom. Loosely speaking, an orbital describes a three-dimensional region around the nucleus in which the electron is most likely to be found. A subshell in an atom is comprised of one or more orbitals, and is denoted by a letter (s, p, d, or f) that describes the shape and energy of the orbital(s). The orbitals in the subshells get progressively more complex and higher in energy in the order listed above. Each energy shell has one or more subshells, and each higher energy shell contains one additional subshell. For example, the first energy shell contains the s subshell, while the second energy shell contains both the s and p subshell, etc.
Electron Configurations
Now that we've described the modern quantum model of the atom, let's see how this is represented as an electron configuration. There are three basic rules: 1) Electrons occupy the lowest energy orbitals available. (This is the Aufbau principle.) Electron subshells are filled in order of increasing energy. The periodic table is logically constructed to reflect this fact, and therefore one can easily determine shell filling for specific atoms based on where they appear on the table. We will detail this in the next section on "Blocks". 2) Electrons in the same subshell occupy available orbitals singly, before pairing up. (This is known as Hund's rule.) 3) There can be no more than two electrons in any given orbital. (This is the Pauli exclusion principle.)
Groups of the periodic table and their characteristics
Recall that each horizontal row in the periodic table is called a period, and each vertical column is called a group (or family). Within any group in the periodic table, all of the elements have the same number of electrons in their outermost shell. For instance, the elements in Group II all have two electrons in their outermost shell. Electrons in an atom's outermost shell are called valence electrons, and its the valence electrons that are primarily responsible for an atom's properties and chemical behavior. The valence-shell electron configuration determines the chemical reactivity of each group in the table. For example, in the noble gas family each element has eight electrons in its outermost shell (ns2np6). Such a closed-shell (fully-filled valence shell) configuration is called an octet and results in great stability (and therefore low reactivity) for an atom. For this reason, noble gases do not generally undergo chemical reactions, so most group VIII elements are inert. Helium is inert as well, but has a closed shell with a stable duet (1s2) of electrons. Other elements experience similar increases in stability upon reaching this stable octet electron configuration, and most chemical reactions can be regarded as the quest for atoms to achieve such closed-shell stability. The alkali metals and alkaline earth metals, for instance, possess one (ns1) or two (ns2) electrons in their valence shells, respectively, and behave as reducing agents (i.e., lose valence electrons) in redox reactions in order to obtain a stable octet, generally as an M+ or M2+ cation. Similarly, the halogens (ns2np5) require only a single electron to achieve a stable octet. To achieve this state in their elemental form, halogens naturally exist as diatomic molecules (e.g., F2) where one electron from each atom is shared in a covalent bond. When combined with other elements, the halogens behave as powerful oxidizing agents (that is, gain electrons); they can become stable either as X- anions or by sharing electrons with other nonmetals (more on bonding in Ch. 5). Reactions between elements on opposite sides of the periodic table can be quite violent. This occurs due to the great degree of stability gained for both elements when the valence electrons are transferred from the metal to the nonmetal. The relative reactivities within these and all other groups can be further explained by the periodic trends detailed in the next section.
Which of the following is NOT an example of a Bohr atom? A) H B) He+ C) Li2+ D) H+
Solution: A Bohr atom is one that contains only one electron. Since H+ has a positive charge from losing the one electron in the neutral atom thereby having no electrons at all, choice D is the answer.
Example 4-18: What's the maximum number of electrons that can go into any s subshell? Any p subshell? Any d? Any f?
Solution: An s subshell has only one possible orbital orientation. Since only two electrons can fill any given orbital, an s subshell can hold no more than 1 × 2 = 2 electrons. A p subshell has three possible orbital orientations (two more than an s subshell). Since again only two electrons can fill any given orbital, a p subshell can hold no more than 3 x 2 = 6 electrons. A d subshell has five possible orbital orientations (two more than a p subshell). Since there are two electrons per orbital, a d subshell can hold no more than 5 × 2 = 10 electrons. Finally, an f subshell has seven possible orbital orientations (two more than a d subshell). Since there are two electrons per orbital, an f subshell can hold no more than 7 x2 = 14 electrons.
Example 4-2: An atom contains 16 protons, 17 neutrons, and 18 electrons. Which of the following best indicates this ion? A) 33Cl- B) 34Cl- C) 33S^2- D) 34S^2-
Solution: Any nucleus that contains 16 protons is sulfur, so we can eliminate choices A and B immediately. Now, because Z = 16 and N = 17, the mass number, A, is Z + N = 16 + 17 = 33. Therefore, the answer is C.
Example 4-30: Which of the following could describe an ion with the same electron configuration as a noble gas? A) An alkali metal that has gained an electron B) A halogen that has lost an electron C) A transition metal that has gained an electron D) An alkaline earth metal that has lost two electrons
Solution: Choice A is wrong since it says "gained" rather than "lost." Choice B is incorrect since it says "lost" rather than "gained." Choice C is also incorrect, because no element in the d block could acquire a noble-gas configuration by gaining a single electron. The answer must be D. If an element in Group II loses two electrons, it can acquire a noble-gas electron configuration. (For example, Mg2+ has the same configuration as Ne, and Ca2+ has the same configuration as Ar.)
Example 4-29: Which of the following elements has a closed valence shell, but not an octet? A) He B) Ne C) Br D) Rn
Solution: Choice A, He, is the correct choice because He, along with H- and Li+, has a completed n= 1 shell with only 2 electrons, since the n= 1 shell can fit only 2 electrons.
Example 4-22: What is the maximum number of electrons that can be present in the n = 3 shell? A) 6 B) 9 C) 12 D) 18
Solution: Every new energy level (n) adds a new subshell. That means that in the first energy level we have only the s subshell, while when n= 2 we have both s and p subshells, and when n = 3, there are s, p, and d subshells. Since there are 1, 3, and 5 s, p, and d orbitals, respectively, for a total of 9 orbitals, and since the maximum number of electrons in an orbital is 2, there can be a maximum of 18 electrons in the n = 3 shell.
Example 4-1: An atom with 7 neutrons and a mass number of 12 is an isotope of what element? A) Boron B) Nitrogen C) Magnesium D) Potassium
Solution: If A = 12 and N = 7, then Z= A - N = 12 - 7 = 5. The element with an atomic number of 5 is boron. Therefore, choice A is the answer.
Example 4-11: Radiolabeled vitamin B12 containing radioactive cobalt- 58 is administered to diagnose a defect in a patient's vitamin-B12 absorption. If 58Co has a halflife of 72 days, approximately what percentage of the radioisotope will still remain in the patient a year later? A) 3% B) 5% C) 8% D) 10%
Solution: One year is approximately equal to 5 halflives of this radioisotope, since 5x 72 = 360 days 1 year. After 5 half-lives, the amount of the radioisotope will drop to (1/2)^5 = 1/32 of the original amount administered. Because 1/32 = 3/100 = 3%, the best answer is choice A.
Example 4-10: Cesium-137 has a half-life of 30 years. How long will it take for only 0.3 g to remain from a sample that had an original mass of 2.4 g? A) 60 years B) 90 years C) 120 years D) 240 years
Solution: Since 0.3 grams is 1/8 of 2.4 grams, the question is asking how long it will take for the radio- isotope to decrease to 1/8 its original amount. We know that this requires 3 half-lives, since 1/2 x 1/2 x 1/2 = 1/8. So, if each half-life is 30 years, then 3 half-lives will be 3(30) = 90 years, choice B.
Example 4-17: Consider two electron transitions. In the first case, an electron falls from n = 4 to n= 2, giving off a photon of light with a wavelength equal to 488 nm. In the second transition, an electron moves from n = 3 to n = 4. For this transition, we would expect that: A) energy is emitted, and the wavelength of the corresponding photon will be shorter than the first transition. B) energy is emitted, and the wavelength of the corresponding photon will be longer than the first transition. C) energy is absorbed, and the wavelength of the corresponding photon will be shorter than the first transition. D) energy is absorbed, and the wavelength of the corresponding photon will be longer than the first transition.
Solution: Since the electron is moving from a lower to higher energy level, we would expect that the atom absorbs energy (eliminating choices A and B). Since the electron transitions between energy levels that are closer together, the ΔE between levels is smaller. By the ΔE=h(c/λ) relationship, we know that energy and wavelength are inversely related. Therefore with a smaller energy change, the wavelength of the associated light will be longer. D is the correct answer.
Example 4-16: The first four electron energy levels of an atom are shown below, given in terms of electron volts. Which of the following gives the energy of a photon that could NOT be emitted by this atom? —————- E4 = -18 eV —————- E3 = -32 eV —————- E2 = -72 eV —————- E1 = -288 eV A) 14 eV B) 40 eV C) 44 eV D) 54 eV
Solution: The difference between E4 and E3 is 14 eV, so a photon of 14 eV would be emitted if an electron were to drop from level 4 to level 3; this eliminates choice A. Similarly, the difference between E3 and E2 is 40 eV, so choice B is eliminated, and the difference between E4 and E2 is 54 eV, so choice D is eliminated. The answer must be C; no two energy levels in this atom are separated by 44 eV.
Of the following atoms/ions, which one contains the greatest number of neutrons? A) 60/28Ni B) 64/29Cu+ C) 64/30Zn D) 64/30Zn2+
Solution: To find N, we just subtract Z (the subscript) from A (the superscript). The atom in choice A has N= 60 - 28 = 32; the ion in choice B has N= 64 - 29 = 35, and the atom or ion in both choices C and D have N= 64 - 30 = 34. Therefore, of the choices given, the ion in choice B contains the greatest number of neutrons.
The Energy Shell
The energy shell (1) of an electron in the quantum model of the atom is analogous to the circular orbits in the Bohr model of the atom. An electron in a higher shell has a greater amount of energy and a greater average distance from the nucleus. For example, an electron in the 3rd shell (n = 3) has higher energy than an electron in the 2nd shell (where n = 2), which has more energy than an electron in the 1st shell (n = 1).
Nuclear stability and radioactivity
The protons and neutrons in a nucleus are held together by a force called the strong nuclear force. It's stronger than the electrical force between charged particles, since for all atoms besides hydrogen, the strong nuclear force must overcome the electrical repulsion between the protons. In fact, of the four fundamental forces of nature, the strong nuclear force is the most powerful even though it only works over extremely short distances, as seen in the nucleus. Unstable nuclei are said to be radioactive, and they undergo a transformation to make them more stable, altering the number and ratio of protons and neutrons or just lowering their energy. Such a process is called radioactive decay, and we'll look at three types: alpha, beta and gamma. The nucleus that undergoes radioactive decay is known as the parent, and the resulting more stable nucleus is known as the daughter.
Atoms
The smallest unit of any element is one atom of the element. All atoms have a central nucleus, which contains protons and neutrons, known collectively as nucleons. Each proton has an electric charge of +1 elementary unit; neutrons have no charge. Outside the nucleus, an atom contains electrons, and each electron has a charge of -1 elementary unit. In every neutral atom, the number of electrons outside the nucleus is equal to the number of protons inside the nucleus. The electrons are held in the atom by the electrostatic attraction of the positively charged nucleus. The number of protons in the nucleus of an atom is called its atomic number, Z. The atomic number of an atom uniquely determines what element the atom is, and Z may be shown explicitly by a subscript before the symbol of the element. For example, every beryllium atom contains exactly four protons, and we can write this as 4Be. A proton and a neutron each have a mass slightly more than one atomic mass unit (1 amu = 1.66x 10^-27 kg) and an electron has a mass that's only about 0.05 percent the mass of either a proton or a neutron. So, virtually all the mass of an atom is due to the mass of the nucleus. The number of protons plus the number of neutrons in the nucleus of an atom gives the atom's mass number, A. If we let N stand for the number of neutrons, then A = Z+ N. In designating a particular atom of an element, we refer to its mass number. One way to do this is to write A as a superscript. For example, if a beryllium atom contains 5 neutrons, then its mass number is 4 + 5 = 9, and we would write this as 9/4Be or simply as 9Be. Another way is simply to write the mass number after the name of the elements, with a hyphen; 9Be is beryllium-9.
Beta decay
There are actually three types of beta decay: ß-, ß+ and electron capture. Each type of beta decay involves the conversion of a neutron into a proton (along with some other particles that are beyond the scope of the MCAT), or vice versa, through the action of the weak nuclear force. Beta particles are more dangerous than alpha particles since they are significantly less massive. They therefore have more energy and a greater penetrating ability. However, they can be stopped by aluminum foil or a centimeter of plastic or glass.