# Early Quantum Theory | General Chemistry 1

Early quantum theory is studied in this chapter: ionization energies, wave model of light, photons and photoelectric effect, wave-particle duality, quantization of the energy of the electron in a hydrogen atom and electronic transitions.

## First Ionization Energies

Ionization energy = minimum energy required to remove an electron from the gaseous atom or ion.
First ionization energy I1 = minimum energy required to remove an electron from a neutral gaseous atom A.
Second ionization energy I2 =  minimum energy required to remove an electron from a gaseous ion A+.

A(g) → A+(g) + e-(g)   (first ionization energy)

A+(g) → A2+(g) + e-(g)    (second ionization)

There is a periodic pattern of the first ionization energies according to the atomic number:
- noble gases have large first ionization energies ⇒ difficult to remove electrons. The electronic structures of the noble gases are very stable.
- alkali metals have relatively low ionization energies ⇒ easy to remove one electron (extremely reactive nature), and so form the electronic structures of the nearest noble gas.

Trend in first ionization energy in the periodic table:
it increases as we go from the left to right across each row and as we go up each column.

## Ionization Energy and Periodicity

The values of successive ionization energies of atoms (first, second, third, etc.) suggest a shell structure.

Electron shell = orbit around an atom nucleus followed by electrons.
Each shell can contain only a fixed number of electrons, and so is associated with a particular range of electron energy.

Core electrons = electrons in filled shells (orbitals) and are closer to the nucleus.
They form the same electronic structure than the previous nearest noble gas in the periodic table.
Valence electrons = electrons in the outermost atomic shell of an atom.
They are the farthest from the positive charge of the nucleus (protons) and thus tend to be easier to remove than core electrons.

## Wave Model of Light

Spectroscopy = analysis of the light emitted or absorbed by substances.
Light = electromagnetic radiation within the portion of the electromagnetic spectrum.
Visible light is only a small portion of this spectrum: 400-750 nm (400nm = blue / 750nm = red).

- gamma rays (< 10-2 nm)
- X rays (10-2 nm – 101 nm)
- ultraviolet light (101 nm – 400 nm)
- infrared light (750 nm – 5 x 105 nm)
- microwaves (5 x 105 nm – 108 nm)
- radio waves (> 108 nm)

Relationship between speed of light, wavelength and frequency:

c = λν

c (in m.s-1) = speed of light = 2.9979 x 108 m.s-1
λ (in m) = wavelength
ν (in s-1) = frequency

Emission Spectra of Atoms:
White light has no gaps ⇒ continuous spectrum
Emission spectra of atoms consist of series of lines: atoms absorb or emit energy at only specific wavelengths.

## Photons and Photoelectric Effect

The energy of light is “quantized” ⇒ can only have certain values.

Energy of A packet of light energy (called “quantum”):

E = hν =  $\frac{\mathrm{hc}}{\mathrm{\lambda }}$

E (in J) = energy associated with a quantum of radiation
h = Planck’s constant = 6.626 x 10-34 J.s
ν (in s-1) = frequency

Energy of a group of photons :

E = nhν

E (in J) = energy associated with a group of photons
n = number of photons

Photoelectric effect:

Ek = 0 (when ν < ν0)
Ek = hν - hν(when ν > ν0)

Ek = kinetic energy of the ejected electrons
ν0 (in s-1) = threshold frequency
ν (in s-1) = frequency of photons

E = hν0 = minimum energy required to eject an electron

## Wave-Particle Duality

Through phenomena observed from light, De Broglie suggested that matter has properties similar to particles and waves and obeys to the equation:

λ = $\frac{\mathrm{h}}{\mathrm{p}}$ = $\frac{\mathrm{h}}{\mathrm{mv}}$

λ (in m) = Broglie wavelength
h = Planck’s constant = 6.626 x 10-34 J.s
p (in g.m.s-1) = momentum = mv (mass x speed)

Electrons also exhibit particle-like + wavelike properties.

## Quantization

The energy of the electron in a hydrogen atom is quantized:

En   ​​​​

En (in J) = energy of the orbital n
n = 1, 2, 3 … = number of the orbital

En values = energy states of electrons in a hydrogen atom
The higher the absolute value of En, the more stable the electron in the orbital n.
n = 1 is the orbital with the more stable electron ⇒ ground state
Other states = excited states

## Electronic Transitions

Atoms emit or absorb electromagnetic radiation when they undergo electronic transitions.

Energy of the transition from initial excited state ni to final state nf (where Ei > Ef ⇒ emission):
Ei = Ef + Ephoton

For the Hydrogen atom:

Ephoton = Ei – Ef
Ephoton = (-2.1799 x 10-18 J) x ($\frac{1}{{{\mathrm{n}}_{\mathrm{i}}}^{2}}$ – $\frac{1}{{{\mathrm{n}}_{\mathrm{f}}}^{2}}$)

and Ephoton = hc/λ

⇒ 1/λ = Ephoton/hc = (-1.097 x 107 m-1) x ($\frac{1}{{{\mathrm{n}}_{\mathrm{i}}}^{2}}$ – $\frac{1}{{{\mathrm{n}}_{\mathrm{f}}}^{2}}$

This is the Rydberg-Balmer equation ⇒ predicts line spectrum of hydrogen atom.
Rydberg constant = 1.097 x 107 m-1