1. Atomic Structure + khan

diamagentic

-all electrons are paired -produces its own magnetic field in the opposite direction (therefore weakly repelled by an external magnetic field)

paramagnetism

-one or more unpaired electrons -pulled into an external magnetic field

The presence of paired or unpaired electrons affects the chemical and magnetic properties of an atom or molecule. Materials composed of atoms with unpaired electrons will orient their spins in alignment with a magnetic field, and the material will thus be weakly attracted to the magnetic field. These materials are considered paramagnetic.

A ferrofluid (colloidal liquid containing a surfactant and paramagnetic particles) is influenced by the magnet beneath a glass slide. The spikes emanating from the fluid contain magnetite (an iron oxide) which is orienting along the magnetic field lines. This is similar to a typical iron filing and magnet demonstration.

Balmer Series

A set of spectral lines that appear in the visible light region when a hydrogen atom undergoes a transition from energy levels n>2 to n=2.

Materials consisting of atoms that have all paired electrons will be slightly repelled by a magnetic field and are said to be diamagnetic. A piece of pyrolytic graphite is suspended in the air over strong neodymium magnets.

All the electrons in this allotrope (configuration) of carbon are paired because of covalent bonding between layers of the material, and are thus opposed to being reoriented. Given sufficiently strong magnetic fields beneath an object, any diamagnetic substance can be made to levitate.

Aufbau principle

An electron occupies the lowest-energy orbital that can receive it

elements with small atomic number (and thus fewer electrons) tend to have most of their electrons living in orbitals near the nucleus.

As we move further down the periodic table, orbitals and energy levels further out from the nucleus begin to fill up with electrons.

KEY CONCEPT 3

At first glance, it may not be clear that the energy (E) is directly proportional to the principal quantum number (n). Take notice of the negative sign, which causes the values to approach zero from a more negative value as n increases (thereby increasing the energy). Negative signs are as important as a variable's location in a fraction when it comes to determining proportionality.

KEY CONCEPT 1

Atomic number (Z) = number of protons Mass number (A) = number of protons + number of neutrons Number of protons = number of electrons (in a neutral atom) Electrons are not included in mass calculations because they are much smaller.

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 or other energy forms to yield excited states.

Because the lifetime of an excited state is brief, the electrons will return rapidly to the ground state, resulting in the emission of discrete amounts of energy in the form of photons.

principal quantum number (n)

First quantum number, designated as the letter "n." It takes on any positive integer value and describes an electron's energy level. An electron with a higher n value is at a higher energy state.

KEY CONCEPT 5

For any principal quantum number n, there will be n possible values for l, ranging from 0 to (n - 1).

KEY CONCEPT 6

For any value of l, there will be 2l + 1 possible values for m1. For any n, this produces n^2 orbitals. For any value of n, there will be a maximum of 2n electrons (two per orbital).

In nature, almost all elements exist as two or more isotopes, and these isotopes are usually present in the same proportions in any sample of a naturally occurring element. The weighted average of these different isotopes is referred to as the atomic weight and is the number reported on the Periodic Table.

For example, chlorine has two main naturally occurring isotopes: chlorine-35 and chlorine-37. Chlorine-35 is about three times more abundant than chlorine-37; therefore, the atomic weight of chlorine is closer to 35 than 37. The half-lives of the different isotopes of the elements; because half-life corresponds with stability, it also helps determine the relative proportions of these different isotopes.

The utility of the atomic weight is that it represents both the mass of the "average" atom of that element, in amu, and the mass of one mole of the element, in grams. A mole is a number of "things" (atoms, ions, molecules) equal to Avogadro's number, N = 6.02 × 10^23 .

For example, the atomic weight of carbon is 12 which means that the average carbon atom has a mass of 12.0 amu (carbon-12 is far more abundant than carbon-13 or carbon-14), and 6.02 × 10^23 carbon atoms have a combined mass of 12.0 grams.

The valence electrons of an atom are those electrons that are in its outermost energy shell, are most easily removed, and are available for bonding. In other words, the valence electrons are the "active" electrons of an atom and to a large extent dominate the chemical behavior of the atom. For elements in Groups IA and IIA (Groups 1 and 2), only the highest s subshell electrons are valence electrons. For elements in Groups IIIA through VIIIA (Groups 13 through 18), the highest s and p subshell electrons are valence electrons.

For transition elements, the valence electrons are those in the highest s and d subshells, even though they do not have the same principal quantum number. For the lanthanide and actinide series, the valence electrons are those in the highest s and f subshells, even though they have different principal quantum numbers. All elements in period three (starting with sodium) and below may accept electrons into their d subshell, which allows them to hold more than eight electrons in their valence shell.

An important corollary from Hund's rule is that half-filled and fully filled orbitals have lower energies (higher stability) than other states. This creates two notable exceptions to electron configuration that are often tested on the MCAT: chromium (and other elements in its group) and copper (and other elements in its group). Chromium (Z = 24) should have the electron configuration [Ar] 4s 3d according to the rules established earlier.

However, moving one electron from the 4s subshell to the 3d subshell allows the 3d subshell to be half-filled: [Ar] 4s 3d (remember that s subshells can hold two electrons and d subshells can hold ten). While moving the 4s electron up to the 3d-orbital is energetically unfavorable, the extra stability from making the 3d subshell half-filled outweighs that cost. Similarly, copper (Z = 29) has the electron configuration [Ar] 4s 3d , rather than [Ar] 4s 3d ; a full d subshell outweighs the cost of moving an electron out of the 4s subshell. Other elements in the same group have similar behavior, moving one electron from the highest s subshell to the highest d subshell. Similar shifts can be seen with f subshells, but they are never observed for the p subshell; the extra stability doesn't outweigh the cost.

The electrons in an atom can 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 energy transition it undergoes. These energy transitions do not form a continuum, but rather are quantized to certain values. Thus, the spectrum is composed of light at specified frequencies.

It is sometimes called a line spectrum, where each line on the emission spectrum corresponds to a specific electron transition. Because each element can have its electrons excited to a different set of distinct energy levels, each possesses a unique atomic emission spectrum, which can be used as a fingerprint for the element. One particular application of atomic emission spectroscopy is in the analysis of stars and planets: while a physical sample may be impossible to procure, the light from a star can be resolved into its component wavelengths, which are then matched to the known line spectra of the elements.

In subshells that contain more than one orbital, such as the 2p subshell with its three orbitals, the orbitals will fill according to Hund's rule, which states that, within a given subshell, orbitals are filled such that there are a maximum number of half-filled orbitals with parallel spins.

Like finding a seat on a crowded bus, electrons would prefer to have their own seat (orbital) before being forced to double up with another electron. Of course, the basis for this preference is electron repulsion: electrons in the same orbital tend to be closer to each other and thus repel each other more than electrons placed in different orbitals.

The atomic mass of an atom (in amu) is nearly equal to its mass number, the sum of protons and neutrons (in reality, some mass is lost as binding energy). Atoms of the same element with varying mass numbers are called isotopes. Isotopes differ in their number of neutrons and are referred to by the name of the element followed by the mass number; for example, carbon-12 or iodine-131.

Only the three isotopes of hydrogen, are given unique names: protium has one proton and an atomic mass of 1 amu; deuterium ("second") has one proton and one neutron and an atomic mass of 2 amu; tritium ("third") has one proton and two neutrons and an atomic mass of 3 amu. Because isotopes have the same number of protons and electrons, they generally exhibit similar chemical properties.

This method works for neutral atoms, but how does one write the electron configuration of an ion? Negatively charged ions (anions) have additional electrons that fill according to the same rules as above; for example, if fluorine's electron configuration is [He] 2s 2p , then F is [He] 2s 2p .

Positively charged ions (cations) are a bit more complicated: start with the neutral atom, and remove electrons from the subshells with the highest value for n first. If multiple subshells are tied for the highest n value, then electrons are removed from the subshell with the highest l value among these.

The third quantum number is the magnetic quantum number and is designated m1. The magnetic quantum number specifies the particular orbital within a subshell where an electron is most likely to be found at a given moment in time. Each orbital can hold a maximum of two electrons. The possible values of m are the integers between -l and +l, including 0. For example, the s subshell, with l = 0, limits the possible m1 values to 0, and because there is a single value of m1, there is only one orbital in the s subshell.

The p subshell, with l = 1, limits the possible m values to −1, 0, and +1, and because there are three values for m1, there are three orbitals in the p subshell. The d subshell has five orbitals (−2 to +2), and the f subshell has seven orbitals (−3 to +3). The shape of the orbitals, like the number of orbitals, is dependent on the subshell in which they are found. The orbitals in the s subshell are spherical, while the three orbitals in the p subshell are each dumbbell-shaped and align along the x-, y-, and z-axes. In fact, the p-orbitals are often referred to as px, py, and pz.

Modern atomic theory postulates that any electron in an atom can be completely described by four quantum numbers: n, l, m1, and m2. Furthermore, according to the Pauli exclusion principle, no two electrons in a given atom can possess the same set of four quantum numbers.

The position and energy of an electron described by its quantum numbers is known as its energy state. The value of n limits the values of l, which in turn limit the values of m1. In other words, for a given value of n, only particular values of l are permissible; given a value of l, only particular values of m1 are permissible. The values of the quantum numbers qualitatively give information about the orientation of the orbitals.

spin quantum number (ms)

The quantum number that has only two possible values, +1/2 and -1/2, which indicate the two fundamental spin states of an electron in an orbital

The second quantum number is called the azimuthal (angular momentum) quantum number and is designated by the letter l. The second quantum number refers to the shape and number of subshells within a given principal energy level (shell). The azimuthal quantum number is very important because it has important implications for chemical bonding and bond angles.

The value of n limits the value of l in the following way: for any given value of n, the range of possible values for l is 0 to (n -1). For example, within the first principal energy level, n = 1, the only possible value for l is 0; within the second principal energy level, n = 2, the possible values for l are 0 and 1. A simpler way to remember this relationship is that the n-value also tells you the number of possible subshells. Therefore, there's only one subshell (l = 0) in the first principal energy level; there are two subshells (l = 0 and 1) within the second principal energy level; there are three subshells (l = 0, 1, and 2) within the third principal energy level, and so on.

Electrons move around the nucleus at varying distances, which correspond to varying levels of electrical potential energy. The electrons closer to the nucleus are at lower energy levels, while those that are further out (in higher shells) have higher energy. The electrons that are farthest from the nucleus have the strongest interactions with the surrounding environment and the weakest interactions with the nucleus.

These electrons are called valence electrons; they are much more likely to become involved in bonds with other atoms because they experience the least electrostatic pull from their own nucleus. Generally speaking, the valence electrons determine the reactivity of an atom. The sharing of these valence electrons in covalent bonds allows elements to fill their highest energy level to increase stability. In the neutral state, there are equal numbers of protons and electrons; losing electrons results in the atom gaining a positive charge, while gaining electrons results in the atom gaining a negative charge. A positively charged atom is called a cation, and a negatively charged atom is called an anion.

Bohr came to describe the structure of the hydrogen atom as a nucleus with one proton forming a dense core, around which a single electron revolved in a defined pathway (orbit) at a discrete energy value. If one could transfer an amount of energy exactly equal to the difference between one orbit and another, this could result in the electron "jumping" from one orbit to a higher-energy one.

These orbits had increasing radii, and the orbit with the smallest, lowest-energy radius was defined as the ground state (n = 1). More generally, the ground state of an atom is the state of lowest energy, in which all electrons are in the lowest possible orbitals. In Bohr's model, the electron was promoted to an orbit with a larger radius (higher energy), the atom was said to be in the excited state. In general, an atom is in an excited state when at least one electron has moved to a subshell of higher than normal energy.

Atomic emission and absorption spectra are complex topics, but the takeaway is that each element has a characteristic set of energy levels. For electrons to move from a lower energy level to a higher energy level, they must absorb the right amount of energy to do so.

They absorb this energy in the form of light. Similarly, when electrons move from a higher energy level to a lower energy level, they emit the same amount of energy in the form of light.

The energy associated with a change in the principal quantum number from a higher initial value n to a lower final value n is equal to the energy of the photon predicted by Planck's quantum theory. Combining Bohr's and Planck's calculations,

This complex-appearing equation essentially says: The energy of the emitted photon corresponds to the difference in energy between the higher-energy initial state and the lower-energy final state.

KEY CONCEPT 4

This equation is nothing new; it is simply derived from conservation of energy by setting the energy of a photon equal to the energy of the electron transition. Note that unlike other equations, this is initial minus final; the negative sign in the equation accounts for absorption and emission. Thus, a positive E corresponds to emission, and a negative E corresponds to absorption.

When an electron is excited to a higher energy level, it must absorb exactly the right amount of energy to make that transition. This means that exciting the electrons of a particular element results in energy absorption at specific wavelengths.

Thus, in addition to a unique emission spectrum, every element possesses a characteristic absorption spectrum. Not surprisingly, the wavelengths of absorption correspond exactly to the wavelengths of emission because the difference in energy between levels remains unchanged. Identification of elements in the gas phase requires absorption spectra.

For a given atom or ion, the pattern by which subshells are filled, as well as the number of electrons within each principal energy level and subshell, are designated by its electron configuration. Electron configurations use spectroscopic notation, wherein the first number denotes the principal energy level, the letter designates the subshell, and the superscript gives the number of electrons in that subshell.

To write out an atom's electron configuration, one needs to know the order in which subshells are filled. Electrons fill from lower- to higher-energy subshells, according to the building-up principle (also called the Aufbau principle), and each subshell will fill completely before electrons begin to enter the next one. The order need not be memorized because there are two very helpful ways of recalling this. The (n + l) rule can be used to rank subshells by increasing energy. This rule states that the lower the sum of the values of the first and second quantum numbers (n + l), the lower the energy of the subshell. This is a helpful rule to remember for Test Day. If two subshells possess the same (n + l) value, the subshell with the lower n value has a lower energy and will fill with electrons first.

Think of the concept of quantized energy as being similar to the change in gravitational potential energy that you experience when you ascend or descend a flight of stairs.

Unlike a ramp, on which you could take an infinite number of steps associated with a continuum of potential energy changes, a staircase only allows you certain changes in height and, as a result, allows only certain discrete (quantized) changes of potential energy.

KEY CONCEPT 2

When an element has two or more isotopes, no one isotope will have a mass exactly equal to the element's atomic weight. Bromine, for example, is listed in the Periodic Table as having a mass of 79.9 amu. This is an average of the two naturally occurring isotopes, bromine-79 and bromine-81, which occur in almost equal proportions. There are no bromine atoms with an actual mass of 79.9 amu.

The fourth quantum number is called the spin quantum number and is denoted by m2. In classical mechanics, an object spinning about its axis has an infinite number of possible values for its angular momentum. However, this does not apply to the electron, which has two spin orientations designated +1/2 and -1/2.

Whenever two electrons are in the same orbital, they must have opposite spins. In this case, they are often referred to as being paired. Electrons in different orbitals with the same m2 values are said to have parallel spins.

Spectroscopic notation refers to the shorthand representation of the principal and azimuthal quantum numbers. The principal quantum number remains a number, but the azimuthal quantum number is designated by a letter: the l = 0 subshell is called s; the l = 1 subshell is called p; the l = 2 subshell is called d; and the l = 3 subshell is called f. Thus, an electron in the shell n = 4 and subshell l = 2 is said to be in the 4d subshell.

Within each subshell, there is a capacity to hold a certain number of electrons, given by: Maximum number of electrons within a subshell = 4l + 2. where l is the azimuthal quantum number. The energies of the subshells increase with increasing l value; however, the energies of subshells from different principal energy levels may overlap. For example, the 4s subshell will have a lower energy than the 3d subshell.

Once you get to copper (Cu) the configuration is

[Ar] 4s1 3d10 it is more stable to have a filled d shell

Once you get to chromium (Cr) the configuration is

[Ar] 4s1 3d5 it is more stable to have a half filled d shell

Hund's rule

all sub shells must have at least 1 e- in each orbital before placing another e- and filling

Protons

are found in the nucleus of an atom. Each proton has an amount of charge equal to the fundamental unit of charge (e = 1.6 × 10^-19 C), and we denote this fundamental unit of charge as "+1 e" or simply "+1" for the proton. Protons have a mass of approximately one atomic mass unit (amu). The atomic number (Z) of an element, is equal to the number of protons found in an atom of that element. As such, it acts as a unique identifier for each element because elements are defined by the number of protons they contain. For example, all atoms of oxygen contain eight protons; all atoms of gadolinium contain 64 protons. While all atoms of a given element have the same atomic number, they do not necessarily have the same mass

Neutrons

are neutral—they have no charge. A neutron's mass is only slightly larger than that of the proton, and together, the protons and the neutrons of the nucleus make up almost the entire mass of an atom. Every atom has a characteristic mass number (A), which is the sum of the protons and neutrons in the atom's nucleus. A given element can have a variable number of neutrons; thus, while atoms of the same element always have the same atomic number, they do not necessarily have the same mass number. Atoms that share an atomic number but have different mass numbers are known as isotopes of the element. For example, carbon (Z = 6) has three naturally occurring isotopes: C, with six protons and six neutrons; C, with six protons and seven neutrons; and C, with six protons and eight neutrons. The convention X is used to show both the atomic number (Z) and the mass number (A) of atom X.

work function

minimum amount of photon energy required to remove a free electron from the surface of a cold metal. The work function can be calculated as the difference between the energy put in by the photon, E, and the kinetic energy of the ejected electron, KE. That is to say, E0=E-KE.

Electrons

move through the space surrounding the nucleus and are associated with varying levels of energy. Each electron has a charge equal in magnitude to that of a proton, but with the opposite (negative) sign, denoted by "−1 e" or simply "-e." The mass of an electron is approximately that of a proton. Because subatomic particles' masses are so small, the electrostatic force of attraction between the unlike charges of the proton and electron is far greater than the gravitational force of attraction based on their respective masses.

pauli exclusion principle

no two electrons in an atom can have the same four quantum numbers

The photon with the shortest wavelength is the one with

the highest energy because Ephoton=hc means that hc=Ephoton.

magnetic quantum number (ml)

the quantum number that indicates the orientation of an orbital around the nucleus ml=-l to +l

Rydberg equation

used to calculate the wavelengths of all the spectral lines of hydrogen

Bohr then related the permitted angular momentum values to the energy of the electron to obtain: E=-(Rh)/(n^2)

where R is the experimentally determined Rydberg unit of energy, equal to 2.18 x 10^-18 J/electron Therefore, like angular momentum, the energy of the electron changes in discrete amounts with respect to the quantum number. A value of zero energy was assigned to the state in which the proton and electron are separated completely, meaning that there is no attractive force between them. Therefore, the electron in any of its quantized states in the atom will have an attractive force toward the proton; this is represented by the negative sign. Ultimately, the only thing the energy equation is saying is that the energy of an electron increases—becomes less negative—the farther out from the nucleus that it is located (increasing n). This is an important point: while the magnitude of the fraction is getting smaller, the actual value it represents is getting larger (becoming less negative).

The electromagnetic energy of these photons can be determined using the following equation: E=hc/λ

where h is Planck's constant, c is the speed of light in a vacuum and λ is the wavelength of the radiation. It is just a combination of two other equations: E = hf and c = f λ.

In 1910, Ernest Rutherford provided experimental evidence that an atom has a dense, positively charged nucleus that accounts for only a small portion of the atom's volume. Eleven years earlier, Max Planck developed the first quantum theory, proposing that energy emitted as electromagnetic radiation from matter comes in discrete bundles called quanta. The energy of a quantum, he determined, is given by the Planck relation: E = hf

where h is a proportionality constant known as Planck's constant, equal to 6.626 × 10^-34 J·s, and f is the frequency of the radiation.

Bohr used Planck's quantum theory to correct certain assumptions that classical physics made about the pathways of electrons. Classical mechanics postulates that an object revolving in a circle, such as an electron, may assume an infinite number of values for its radius and velocity. The angular momentum (L = mvr) and kinetic energy (k=1/2mv^2) of the object could therefore take on any value. However, by incorporating Planck's quantum theory into his model, Bohr placed restrictions on the possible values of the angular momentum. Bohr predicted that the possible values for the angular momentum of an electron orbiting a hydrogen nucleus could be given by: L=nh/2(pie)

where n is the principal quantum number, which can be any positive integer, and h is Planck's constant. Because the only variable is the principal quantum number, the angular momentum of an electron changes only in discrete amounts with respect to the principal quantum number. Note the similarities between quantized angular momentum and Planck's concept of quantized energy.

While Bohr's model marked a significant advancement in the understanding of the structure of atoms, his model ultimately proved inadequate to explain the structure and behavior of atoms containing more than one electron. The model's failure was a result of not taking into account the repulsion between multiple electrons surrounding the nucleus. Modern quantum mechanics has led to a more rigorous and generalizable study of the electronic structure of atoms. The most important difference between Bohr's model and the modern quantum mechanical model is that Bohr postulated that electrons follow a clearly defined circular pathway or orbit at a fixed distance from the nucleus, whereas modern quantum mechanics has shown that this is not the case.

Rather, we now understand that electrons move rapidly and are localized within regions of space around the nucleus called orbitals. The confidence by which those in Bohr's time believed they could identify the location (or pathway) of the electron was now replaced by a more modest suggestion that the best we can do is describe the probability of finding an electron within a given region of space surrounding the nucleus. In the current quantum mechanical model, it is impossible to pinpoint exactly where an electron is at any given moment in time. This is expressed best by the Heisenberg uncertainty principle: It is impossible to simultaneously determine, with perfect accuracy, the momentum and the position of an electron. If we want to assess the position of an electron, the electron has to stop (thereby removing its momentum); if we want to assess its momentum, the electron has to be moving (thereby changing its position).

angular momentum quantum number (l)

Symbol- L -tells you the shape of the orbital . The # of possible shapes is = to the value of (n) -Value of "L" is 0 and all positive integers less than or = to n-1.

The shapes of the orbitals in the d and f subshells are much more complex, and the MCAT will not expect you to answer questions about their appearance. The shapes of orbitals are defined in terms of a concept called probability density, the likelihood that an electron will be found in a particular region of space.

Take a look at the 2p block in the Periodic Table. As mentioned above, 2p contains three orbitals. If each orbital can contain two electrons, then six electrons can be added during the course of filling the 2p-orbitals. As atomic number increases, so does the number of electrons (assuming the species is neutral). Therefore, it should be no surprise that the p block contains six groups of elements. The s block contains two elements in each row of the Periodic Table, the d block contains ten elements, and the f block contains fourteen elements.

The first quantum number is commonly known as the principal quantum number and is denoted by the letter n. This is the quantum number used in Bohr's model that can theoretically take on any positive integer value. The larger the integer value of n, the higher the energy level and radius of the electron's shell. Within each shell, there is a capacity to hold a certain number of electrons, given by: Maximum number of electrons within a shell = 2n^2 where n is the principal quantum number.

The difference in energy between two shells decreases as the distance from the nucleus increases. For example, the energy difference between the n = 3 and the n = 4 shells is less than the energy difference between the n = 1 and n=2 shells. Remember that electrons do not travel in precisely defined orbits; it just simplifies the visual representation of the electrons' motion

photoelectric effect

The emission of electrons from a material when light of certain frequencies shines on the surface of the material

The Bohr model of the hydrogen atom explained the atomic emission spectrum of hydrogen, which is the simplest emission spectrum among all the elements. The group of hydrogen emission lines corresponding to transitions from energy levels n ≥ 2 to n = 1 is known as the Lyman series.

The group corresponding to transitions from energy levels n ≥ 3 to n = 2 is known as the Balmer series, and includes four wavelengths in the visible region. The Lyman series includes larger energy transitions than the Balmer series; it therefore has shorter photon wavelengths in the UV region of the electromagnetic spectrum. The Paschen series corresponds to transitions from n ≥ 4 to n = 3.