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1.1 The wavelength of the main line in the sodium atomic spectrum line is 589 nm. What are the frequency and the wavenumber for this line? What is the energy of one photon of this wavelength?
Using 
and a value of c of 3.00 x 108 m s−1 to three significant figures. ν = (3.00 x 108 m s−1 )/ (589 x 10−9 m) = 5.09 x10 14 s−1. The wavenumber, 
, is the number of waves per unit length so for a wavelength of 589 x 10−9 m, 
= 1700000 m−1 = 17000 cm−1 . The energy can be obtained from E = hν: therefore E = 6.626 x 10−34 J s x 5.09 x10 14 s−1 = 3.37 x 10−19 J.
1.2 (a) A laser emits light with a frequency of 4.12 x1014 s−1. Calculate the energy of one photon.
1.2 (b) If the laser emits a pulse containing 2.0 x1018 photons of this radiation, what is the total energy of that pulse?
1.2 (c) If the laser emits 1.3 x10−2 J of energy during a pulse, how many photons are emitted?
(a) The energy can be obtained from E = hν: therefore E = 6.626 ´ 10−34 J s x 4.12 x1014 s−1 = 2.73 x10−19 J.
(b) The total energy will be 2.0 x1018 x 2.73 x10−19 J = 0.546 J.
(c) The number of photons will be 1.3 x10−2 J / 2.73 x10−19 J = 4.76 x 1016.
1.3 What is the wavelength of an electron moving with a speed of 5.97 x106 ms−1 ? (me = 9.11 x10−31 kg).
The de Broglie relationship can be used to calculate this 
So
1.4 The structure of [Cu(OH2)6](BrO3)2 determined using single X-ray diffraction at room temperature shows the copper atom to have a regular copper environment with six equal Cu-O bond lengths while a study using X-ray spectroscopy shows a distorted environment with two long and four shorter Cu-O distances. Describe a possible reason for these observations.
These differing observations derive from the time scales of each technique and the length of time over which they sample the structure in an experiment. The origin of the effect observed here is known as a dynamic Jahn-Teller effect. We would expect Cu(II) as a d9 ion to adopt a distorted octahedral environment with, most often, axial elongation of the octahedron. This is what is observed using X-ray spectroscopic techniques where the interaction time is around 10−17 – 10−18 s. A “snapshot” of the geometry is an axially distorted octahedron with two long axial and four shorter Cu-O distances. X-ray diffraction data have the same interaction time scale but the crystallography technique collects data over a whole crystal containing around 1019 copper complexes and typically over a period of several hours. The X-ray diffraction technique, therefore, samples all possible positions and orientations of the [Cu(OH2)6]2+ ion. This species undergoes a dynamic Jahn-Teller effect in the crystal where the elongation can take place along any of the x, y, or z directions and the individual molecules move rapidly between these different stretched orientations. The determined crystal structure is therefore an average of these which has 6 equivalent Cu-O bond lengths. Note that X–ray spectroscopy samples the shape of the molecules and the orientation of the elongation does not affect the measured Cu-O distances.
1.5 What experimental characterisation methods could be used to investigate the following:
(a) Non-destructive identification of a small amount of an unknown metal oxide in a forensic investigation?
Powder X-ray diffraction would achieve this. It is non-destructive and requires only a few milligrams of sample. The powder X-ray diffraction pattern could be compared with known patterns in a database to identify the unknown metal oxide. See Chapter 2 Section 2.7.
(b) Determining whether O-H or O-D bonds vibrate at a higher frequencies (wavenumbers)?
Vibrational spectroscopy; and infra-red spectroscopy is most commonly available technique and instrumentation. O-H bonds typically exhibit stretching frequencies at higher frequencies (around 3500 cm−1) than O-D bonds (around 2550 cm−1). Though the position is normally reversed for bending motions. See Chapter 4 Section 4.3.
(c) Whether a sample is dimethylsilane ((CH3)2SiH2) or ethylsilane (C2H5SiH3)?
1H NMR spectroscopy would distinguish these showing two type of proton in (CH3)2SiH2 and 3 types in C2H5SiH3, see Chapter 3.