Quantum Theory and the Electronic Structure of Atoms

Wavelength

is the distance between identical points on

successive waves.

Amplitude

is the vertical distance from the midline of a

wave to the peak or trough.

Frequency

(ν) is the number of waves that pass through a

particular point in 1 second (Hz = 1 cycle/s).

Speed

(u) of the wave = λ x ν

Maxwell (1873),

proposed that visible light consists of

electromagnetic waves.

Electromagnetic

radiation

is the emission

and transmission of energy

in the form of

electromagnetic waves.

Speed of light

(c) in vacuum = 3.00 x 108 m/s

All electromagnetic radiation

λ x ν = c

n (principal quantum number)

= 1,2,3,…

RH (Rydberg constant)

= 2.18 x 10-18J

e-

can only have specific

(quantized) energy

values

De Broglie (1924)

reasoned

that e- is both particle and

wave.

u

= velocity of e-

m

= mass of e-

Laser light

is (1) intense, (2) monoenergetic, and (3) coherent

λe

= 0.004 nm

Schrodinger Wave Equation

wrote an equation that

described both the particle and wave nature of the e-

Wave function (Ψ) describes:

energy of e- with a given Ψ. probability of finding e- in a volume of space.

Schrodinger’s equation

can only be solved exactly

for the hydrogen atom. Must approximate its

solution for multi-electron systems.

Actual Schrodinger Wave Equation

Ψ = fn(n, l, ml, ms)

1s orbital

Where 90% of the

e- density is found

for the

angular momentum quantum number l

l = 0 s orbital

l = 1 p orbital

l = 2 d orbital

l = 3 f orbital

magnetic quantum number ml

if l = 1 (p orbital), ml = -1, 0, or 1

if l = 2 (d orbital), ml = -2, -1, 0, 1, or 2

principal quantum number n

n = 1, 2, 3, 4, ….

n=1

n=2

n=3

7.6

distance of e- from the nucleus

spin quantum number ms

ms = +½ or -½

Pauli exclusion principle

no two electrons in an atom

can have the same four quantum numbers.

Shell

electrons with the same value of n

Subshell

electrons with the same values of n and l

Orbital

electrons with the same values of n, l, and ml

How many electrons can an orbital hold?

2

Energy of orbitals in a single electron atom

Energy only depends on principal quantum number n

Energy of orbitals in a multi-electron atom

Energy depends on n and l

Hund’s rule

The most stable arrangement of electrons

in subshells is the one with the greatest

number of parallel spins

Electron configuration

is how the electrons are

distributed among the various atomic orbitals in an

atom.

Paramagnetic

unpaired electrons

Diamagnetic

all electrons paired

In 1868, Pierre Janssen

detected a new dark line in the solar

emission spectrum that did not match known emission lines. Mystery element was named Helium

In 1895, William Ramsey

discovered helium in a mineral of

uranium (from alpha decay).