Chapter 7

Electromagnetic Radiation  aka. Radiant energy or light  A form of energy having both wave and particle characteristics  Moves through a vacuum at the speed of light  3.00 x 10 8 m/s

 Symbol  λ  The distance between two adjacent peaks of a wave  Units - nm

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

 Frequency  ν  The number of waves (or cycles) that pass a given point in a second Frequency

 Inversely related c = λ ν c = 3.00 x 10 8 m/s λ = wavelength (m) 1 m = 1 x 10 9 nm ν = frequency (s -1 or Hz)

 A certain violet light has a wavelength of 413 nm. What is the frequency of the light?  c = λ v (3.00 x 10 8 m/s) = 413 nm ( 1 m v 1 x 10 9 nm v = 7.26 x 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 by E = h ν E = energy in J h = Plank’s constant (6.626 x J s) ν = frequency in s -1 or Hz

 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 10 8 m/s)/(555nm 1 m/1 x 10 9 nm) = 5.41 x /s ◦ E = h ν = (6.626 x Js)(5.41 x /s) = 3.58 x J ◦ X J/mol = (3.58 x J/photon)(6.02 x photons/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 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

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 = x J Z 2 n 2 n = energy level Z = 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 electron energy 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 = x J Z 2 n 2 = x J 1 2 = x J 1 2  E = x J Z 2 n 2 = x J 1 2 = x J 2 2 ∆E = ( x J) – ( x J) = x J

E = h ν x J = ( x J s)( ν) ν = 2.46 x s -1 λ = c / ν = (3.00 x 10 8 m/s) / (2.46 x s -1 ) = x m = 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

 x*  (mv) > h/4   x = uncertainty in position  (mv)=uncertainty in momentum h = Planck’s constant

 The better we know a particle’s position, the less accurately we know its momentum  Limitation very small for large particles