Quantum Numbers and Atomic Orbital, Electron Configurations and the Periodic Table

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n

is a positive integer representing the principle quantum number

l

is an integer representing the angular momentum

m_l

is an integer from-l through 0 to +l, called the magnetic quantum number, prescribing the 3D orientation of the orbital of in the space around the nucleus.

m_s

indicates the spin of the electron and is only +1/2 or -1/2.

The square of the wave function gives the

probability of electron density

probability density

a measure of the probability of finding an electron of a particular energy in a particular region of the atom.

An atomic orbital is specified by

three quantum numbers. they are: principle quantum number (n), angular momentum (l), magnetic quantum number (m_l).

Indicates the relative size of the orbital (and therefore the relative distance from the nucleus)

n

an integer from 0 to (n-1)

l

indicates the shape of the orbital

l

a positive integer
Indicates the relative size of the orbital and relative distance from the nucleus

n

an integer from 0 to (n-1)

l

an integer with values from -l to +l

m_l

Indicates the spatial orientation of the orbital

m_l

Level

energy levels (shells) , given by n value

the smaller the n value the lower the ...

energy level and the greater the probability the electron is closer to the nucleus

Sublevel (subshells)

levels are divided into these, given by the l value

l = 0 is an (what subshell)

s subshell

l = 2 is a (what subshell)

d subshell

l = 1 is a (what subshell)

p subshell

l = 3 is an (what subshell)

f subshell

Orbital

described by each combination of n, l, and ml, specifies the size (energy), shape, and spatial orientation of one of the atom's orbitals

Ψ

energy of the atom

atomic orbital

mathematical description of the electrons wavelike behavior in an atom.

Ψ2

probability density

S orbitals are

spherical

p orbitals are

two-lobed

d orbitals are

multi-lobed

Each electron in any atom is described completely by a set of

4 quantum numbers: n,l,m_l, and m_s

The first three quantum numbers of an electron n, l, and m_l describe the

orbital

The fourth quantum number describes the

electron spin

Pauli's exclusion principle

No two electrons in the same atom can have the same four quantum numbers

An atomic orbital

what can hold a maximum of two electrons, with a must have opposing spins.

The energies of atomic orbitals are affected by

nuclear charge (Z), and shielding by other electrons

A higher nuclear charge increases

nucleus-electron interactions and lowers sublevel energy

Shielding by other electrons reduces

the full nuclear charge to an effective nuclear charge (Zeff)

Zeff

is the nuclear charge an electron actually experiences

sublevel energies

Orbital shape affects

Electrostatic effects

attraction of opposite charges and repulsion of like charges

Energy states of many-electron systems are affected by ________ which gives rise to ______.

electron-electron repulsions/the splitting of energy levels into sublevels

Electrons in the same energy level shield

each other to an extent

Electrons in inner energy levels shield

the outer electrons very effectively.

The further from the nucleus an electron is, the lower the

Zeff for that particular electron. (effective nuclear charge)

Penetration increases ______ and decreases _______

nuclear attraction/shielding

Orbital shape causes electrons in some orbitals to ____________ close to the nucleus.

Orbital shape causes electrons in some orbitals to "penetrate" close to the nucleus.

Each energy level is split into _______ of differing __________

sublevels/energy

Splitting is caused by _____ and its effect on

penetration/shielding

, a lower l value indicates

a lower energy sublevel.

The aufbau principle

electrons are always placed in the lowest energy sublevel available

Hund's rule

specifies that when orbitals of equal energy are available, the lowest energy electron configuration has the maximum number of unpaired electrons with parallel spins

Elements in the same group of the periodic table have the same

outer electron configuration

Elements in the same group of the periodic table exhibit similar

chemical behavior

Similar outer electron configurations correlate with similar

chemical behavior

Inner (core) electrons are those an atom has in common with

the pervious noble gas and any completed transition series

Outer electrons are those in the _______ energy level.

highest

Valence electrons are those involved in forming

compounds

For main group elements, the valence electrons are the

outer electrons

For transition elements, the valence electrons include the outer electrons and

any (n-1)d electrons

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