Chapter 7. Electromagnetic Radiation aka. Radiant energy or light A form of energy having both...

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Transcript of Chapter 7. Electromagnetic Radiation aka. Radiant energy or light A form of energy having both...
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 gammarays 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 (s1 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 1034J
• s) ν = frequency in s1 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 1034J•s)(5.41 x 1014 1/s)
= 3.58 x 1019J◦ X J/mol = (3.58 x 1019J/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 1018J • 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 1018J • Z2
n2
= 2.178 x 1018J •12 = 2.178 x 1018 J 12
E = 2.178 x 1018J • Z2
n2
= 2.178 x 1018J •12 = 5.445 x 1019 J 22
∆E = (5.445 x 1019 J) – (2.178 x 1018 J)= 1.633 x 1018 J
E = h ν1.633 x 1018 J = (6.626 x 1034J • s)(ν)ν = 2.46 x 1015 s1
λ = c / ν = (3.00 x 108 m/s) / (2.46 x 1015 s1) = 1.216 x 107m = 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