# 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).

n

l

l

n

l

m_l

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

s subshell

d subshell

p 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

spherical

two-lobed

multi-lobed

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

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

orbital

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.

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

highest

compounds

outer electrons

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

any (n-1)d electrons

Example: