ATOMIC STRUCTUREChapter 7

Electromagnetic Radiationaka. Radiant energy or lightA form of energy having both wave and particle characteristicsMoves through a vacuum at the speed of light 3.00 x 108 m/s

The Wave Nature of Light

Symbol λThe distance between two adjacent peaks of a wave

Units - nm

Wavelength

Electromagnetic Spectrum

Waves in the electromagnetic spectrum vary in size from very long radio waves the size of buildings, to very short gamma-rays smaller than the size of the nucleus of an atom

Electromagnetic Spectrum

The Visible Spectrum

FrequencyνThe number of waves (or cycles) that pass a given point in a second

Frequency

Inversely relatedc = λ • νc = 3.00 x 108 m/sλ = wavelength (m)

1 m = 1 x 109 nmν = frequency (s-1 or Hz)

Relationship?

A certain violet light has a wavelength of 413 nm. What is the frequency of the light?

c = λv(3.00 x 108 m/s) = 413 nm ( 1 m v

1 x 109nmv = 7.26 x 1014 Hz

A quantum (or photon) is a specific particle of light energy ◦Can be emitted or absorbed as

electromagnetic energy◦The energy of a photon can be

determined byE = h ν

E = energy in Jh = Plank’s constant (6.626 x 10-34J

• s) ν = frequency in s-1 or Hz

Quantized Energy and Photons

What is the frequency, energy of a single photon, and the energy of a mole of photons of light having a wavelength of 555 nm?◦ ν = c /λ = (3.00 x 108 m/s)/(555nm • 1 m/1 x 109nm)

= 5.41 x 1014 1/s◦ E = h ν = (6.626 x 10-34J•s)(5.41 x 1014 1/s)

= 3.58 x 10-19J◦ X J/mol = (3.58 x 10-19J/photon)(6.02 x 1023photons/mol)

= 216,000 J/mol or 216 kJ/mol

Atomic emission spectrum ◦ aka line spectrum◦ A pattern of discrete lines of different

wavelengths ◦ Each element produces a characteristic and

identifiable pattern

Line Spectra and the Bohr Model

HYDROGEN

The Bohr model explains the lines on the emission spectrum of hydrogen.◦Energy is quantized Only in discrete amounts Whole number multiples of h ν

◦Electrons move in circular, fixed energy orbits Ground state – lowest energy state Excited state – higher than ground state

The Bohr Model of an Atom

•According to Bohr's model only certain orbits were allowed which means only certain energies are possible. •These energies naturally lead to the explanation of the hydrogen atom spectrum.

E = -2.178 x 10-18J • Z2

n2

n = energy levelZ = nuclear charge (1 for hydrogen)

*the negative sign means energy of the electron bound to the nucleus is lower than it would be if the electron were away from the nucleus

n = ∞ there is no interaction between nucleus and

electronenergy is zero

Calculate the energy required to excite the hydrogen electron from level n = 1 to n = 2. Also calculate the wavelength of light that must be absorbed by a hydrogen atom in its ground state to reach this excited state.

E = -2.178 x 10-18J • Z2

n2

= -2.178 x 10-18J •12 = -2.178 x 10-18 J 12

E = -2.178 x 10-18J • Z2

n2

= -2.178 x 10-18J •12 = -5.445 x 10-19 J 22

∆E = (-5.445 x 10-19 J) – (-2.178 x 10-18 J)= 1.633 x 10-18 J

E = h ν1.633 x 10-18 J = (6.626 x 10-34J • s)(ν)ν = 2.46 x 1015 s-1

λ = c / ν = (3.00 x 108 m/s) / (2.46 x 1015 s-1) = 1.216 x 10-7m = 121.6 nm

There is a fundamental limitation to just how precisely we can know both the position and momentum of a particle at a give time

Heisenberg Uncertainty Principle

x*(mv) > h/4

x = uncertainty in position(mv)=uncertainty in momentumh = Planck’s constant

The better we know a particle’s position, the less accurately we know its momentum

Limitation very small for large particles