Ch1: Atomic Structure - Kaplan MCAT Gen Chem

protons

• in the nucleus

• +1

• mass of 1 amu

atomic number (Z)

number of protons found in an atom of that element

• identifier of each element (at top of each square in periodic table)

neutrons

• no charge

• mass is slightly larger than 1 amu

mass number (A)

sum of the protons and neutrons in the atom’s nucleus

isotopes

atoms that share an atomic number (same element) but have different mass numbers

• same # of protons, different # of neutrons

• bc they have the same number of protons and electrons, they generally exhibit similar chemical properties

atomic weight

weighted average of all naturally occurring isotopes (at bottom of each square in periodic table)

electrons

move through the space surrounding the nucleus

• varying levels of energy

• -1

• negligible mass

which is greater?

the electrostatic force of attraction between the unlike charges of the proton or electron

OR

the gravitational force of attraction based on their respective masses?

the electrostatic force of attraction between the unlike charges of the proton or electron is far greater

• because subatomic particles’ masses are so small

the electrons closer to the nucleus are at (higher/lower?) energy levels?

lower energy levels

the electrons further away from the nucleus (in higher shells) have (higher/lower?) energy

higher energy

valence electrons

electrons that are farthest from the nucleus

• strongest interactions with the surrounding environment

• weakest interactions with the nucleus

• much more likely to become involved in bonds with other atoms

why are valence electrons much more likely to become involved in bonds with other atoms?

they experience the least electrostatic pull from their own nucleus

sharing or transferring of valence electrons in bonds allows elements to…

fill their highest energy level to increase stability

cation

positively charged atom

anion

negatively charged atom

atomic mass of an atom (in amu)

nearly equal to its mass number

• the sum of protons and neutrons

isotopes of hydrogen

• protium

• deuterium

• tritium

protium

isotope of hydrogen

• 1 proton

• mass=1 amu

deuterium

isotope of hydrogen

• 1 proton

• 1 neutron

• mass=2 amu

tritium

isotope of hydrogen

• 1 proton

• 2 neutrons

• mass=3 amu

half life indicates what?

stability

• helps determine relative proportions of different isotopes

when an element has two or more isotopes, what does that mean in terms of mass and atomic weight?

when an element has two or more isotopes, no one isotope will have a mass exactly equal to the element’s atomic weight

utility of atomic weight

• represents mass of the “average” atom of that element in amu

• represents the mass of one mole of the element in grams

Avogadro’s number

6.02×10²³

mole

number of “things” (atoms, ions, molecules) equal to Avogadro’s number

Rutherford

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

Planck

in 1921 Max Planck developed the first quantum theory, proposing:

• energy emitted as electromagnetic radiation from matter comes in distinct bundles called quanta

how is the energy of a quantum calculated?

Planck reaction:

E=hf

Planck reaction

E=hf

where:

• h= Planck’s constant

• f (sometimes written as v)= frequency of the radiation

Planck’s constant (h)

6.626×10^-34 J*s

Bohr’s idea

• hydrogen atom consists of a central proton around which an e- travels in a circular orbit

• centripetal force acting on the e- as it revolves around the nucleus is created by electrostatic force between p+ and e-

Bohr angular momentum equation

L = nh/2π

where:

• n=principal quantum number (any + integer)

• h=Planck’s constant

angular momentum changes how?

angular momentum of an electron changes only in discrete amounts with respect to the principal quantum number

• because the only variable is the principal quantum number

Bohr energy of electron equation

E = -(R_H)/(n²)

Rydberg unit of energy (R_H)

2.18×10^-18 J/electron

how does the energy of the electron change?

the energy of the electron changes in discrete amounts with respect to the quantum number

Bohr’s description of the structure of a hydrogen atom

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

ground state

state of lowest energy, in which all electrons are in the lowest possible orbitals

excited state

at least one electron has moved to a subshell of higher than normal energy

how is Bohr’s model incorrect?

electrons are not restricted to specific pathways, but tend to be localized in certain regions of space

mnemonic: as electrons go from a lower → higher energy level, they get AHED

Absorb light

Higher potential

Excited

Distant (from the nucleus)

electromagnetic energy of photons equation

E = hc/λ

• h=Planck’s constant

• c= speed of light in a vacuum (3.00×10⁸ m/s)

• λ= wavelength of radiation

line spectrum

• spectrum is composed of light at specified frequencies

• each line on the emission spectrum corresponds to a specific electron transition

atomic emission spectrum

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

Lyman series

the group of hydrogen emission lines corresponding to transitions from energy levels n≥2 → n=1

Balmer series

the group of hydrogen emission lines corresponding to transitions from energy levels n≥3 → n=2

• includes 4 wavelengths in the visible spectrum

compare Lyman series and Balmer series

Lyman series (n≥2 → n=1) includes larger energy transitions than the Balmer series (n≥3 → n=2)

• so Lyman series has shorter photon wavelengths in the UV region of the electromagnetic spectrum

Paschen series

corresponds to transitions from n≥2 → n=3

how does energy relate to wavelength?

energy is inversely proportional to wavelength

E = hf = hc/λ

which equation shows that:

the energy associated with a change in the principal quantum number from a higher initial value (n_i) to a lower final value (n_f)

=

the energy of the photon

E = hc/λ = -R_H [(1/n_i²) - (1/n_f²)]

• the energy of the emitted photon corresponds to the difference in energy between the higher-energy initial state and the lower-energy final state

positive E value corresponds to:

emission

negative E value corresponds to:

absorption

ΔE for absorption or emission between any two energy levels is:

ΔE for absorption or emission between any two energy levels is the same according to the conservation of energy

• this is also the same as the energy of the photon of light absorbed or emitted

absorption spectrum

every element possesses a characteristic absorption spectrum

• exciting the electrons of a particular element results in energy absorption at specific wavelengths

• wavelengths of absorption correspond exactly to the wavelengths of emission bc the difference in energy levels is the same

orbitals

electrons move rapidly and are localized within regions of space around the nucleus called orbitals

Heisenberg uncertainty principle

it is impossible to simultaneously determine, with perfect accuracy, the momentum and the position of an electron

Pauli exclusion principle

no two electrons in a given atom can possess the same set of four quantum numbers

energy state

the position and energy of an electron described by its quantum numbers

principal quantum number: n

quantum number used in Bohr’s model that can theoretically take on any positive integer value

• shell #

• size and energy of atomic orbital

the larger the integer value of n, the higher the:

• higher energy level

• larger radius of e-’s shell

equation for max # of e-s within a shell

2n²

the difference in energy between two shells [increases/decreases?]

as the distance from the nucleus [increases/decreases?]

difference in energy between two shells decreases as the distance from the nucleus increases

• because the energy difference is a function of [1/n_i² - 1/n_f²]

azimuthal (angular momentum) quantum number: l

refers to the shape and number of subshells within a given principal energy level (shell)

how does the value of n limit the value of l

for any given value of n, the range of possible values for l is 0→(n-1)

if l=0

s

if l=1

p

if l=2

d

if l=3

f

spectroscopic notation

l=0 →s

l=1 →p

l=2 →d

l=3 →f

max # of e-s within a subshell equation

4l + 2

magnetic quantum number: m_l

specifies the particular orbital within a subshell where an electron is most likely to be found at a given moment in time

• possible values are integers between -l and +l, including 0

each orbital can hold a max of how many e-s?

2

the shape of the orbital is dependent on what?

the subshell in which they are found

shape of orbitals in the s subshell

spherical

shape of orbitals in the p subshell

dumbbell shaped

• align along the x-, y-, and z- axes (p_x, p_y, p_z)

probability density

the likelihood that an e- will be found in a particular region of space

• the shapes of orbitals are defined in terms of probability density

the s block contains how many elements?

2 elements in each row of the periodic table

the p block contains how many elements?

6 groups of elements

the d block contains how many elements?

10

the f block contains how many elements?

14

spin quantum number: m_s

electron has two spin orientations designated +1/2 and -1/2

paired electrons

whenever two e-s are in the same orbital, they must have opposite spins

• in this case they are paired

parallel spins

electrons in different orbitals with the same m_s values

electron configuration

for a given atom or ion, the pattern by which subshells are filled, as well as the number of e-s within each principal energy level and subshell are designated by its electron configuration

• first number is principal energy level

• letter is subshell

• subscript gives number of e-s in that subshell

Aufbau principle

electrons fill from lower to higher energy subshells

• each subshell will fill completely before electrons begin to enter the next one

n + l rule

the lower the sum of the values of the 1st and 2nd quantum #s, n+l, the lower the energy of the subshell

• if two subshells have the same n+l value, the one with the lower n value has lower energy (and will fill with e-s first)

• lower energy fill up first

lowest s subshell

1s

lowest p subshell

2p

lowest d subshell

3d

lowest f subshell

4f

Hund’s rule

within a given subshell, orbitals are filled such that there are a maximum number of half-filled orbitals with parallel spins

• this is true in subshells that contain more than one orbital

• the basis for this is electron repulsion

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

half-filled and fully filled orbitals have [higher/lower?] energies than other states

lower energies

• meaning higher stability

important exceptions to electron configuration

1. chromium (and other elements in its group)

2. copper (and other elements in its group)

why is chromium (and other elements in its group) an exception to electron configuration?

• chromium (Z=24) should be [Ar]4s²3d⁴ according to the rules

• BUT moving 1 e- from 4s→3d allows the 3d subshell to be half filled: [Ar]4s¹3d⁵

• extra stability from making 3d half filled outweighs the cost of it being energetically unfavorable

why is copper (and other elements in its group) an exception to electron configuration?

• copper (Z=29) has the electron configuration: [Ar]4s¹3d¹⁰ instead of [Ar]4s²3d⁹

• full d subshell outweighs the cost of moving an e- out of the 4s subshell

in which subshell does the extra stability of the shift NOT outweigh the cost?

p subshell

paramagnetic

materials composed of atoms with unpaired electrons will orient their spins in alignment with a magnetic field

• the material will thus be attracted to the magnetic

• paramagnetic = magnetic field will cause parallel spins in unpaired e-s and cause attraction

diamagnetic

materials consisting of atoms that have only paired electrons will be slightly repelled by a magnetic field

• given sufficiently strong magnetic fields beneath an object, any diamagnetic substance can be made to levitate

allotrope

configuration