## Planck's Equation Q1 ANSWERS

### Fill in all the gaps, then press "CHECK" at any time,as long as you are not bothered about the score, but interested in self-tuition! You can printout, do later and come back for the answers. For convenience Greek letters are NOT used in formulae and calculations, so please use ...
c = velocity of light = 3.00 x 108 ms-1
w = wavelength in m ( properly!, note 1 nanometre or 1nm = 10-9m)
f = frequency in Hz ( properly!)
E = quantum energy of a single photon in J
h = Planck Constant = 6.63 x 10-34 JHz-1
Avogadro Constant = L = 6.02 x 1023 mol-1
Bond enthalpies kJ mol-1: C-H 413; C-Br 290; C-Cl 346

Answer all question parts to 2 decimal places except where indicated in [sf] or an integer power.
Q1. Bromo and chloro compounds in the atmosphere can lead to ozone depletion. In a laboratory experiment ultraviolet light (uv) of wavelength 390nm was passed through bromochloromethane CH2BrCl.

(a) A little conversion job! The wavelength of the uv light is
= 390 x 10-9 = 3.90 x 10-7 m

(b)
(i) To interconvert wavelength and frequency we use the formula:
c = w x f, and so f = c / w
(ii) The frequency of the uv light is
3.00 x 108 / 3.90 x 10-7 = 7.69 x 1014 Hz

(c)
(i) Planck's Equation, E = h x f, gives us the energy of the photon.
(ii) The quantum energy of each uv photon is
6.63 x 10-34 x 7.69 x 1014 = 5.10 x 10-19 J

(d) The energy per mole of photons ...
(i) = 5.10 x 10-19 x 6.02 x 1023 = 3.07 x 105 J
(ii) = 307 kJ [3sf]

(e) Which bond will undergo homolytic fission when uv light photons strike the bromochloromethane molecules? C-H, C-Br or C-Cl?: C-Br

(f) What is the minimum energy needed to break one C-Cl bond?
346[3sf] x 1000[4sf] = 3.46 x 105 J for 1 mole of bonds
Energy to break one bond is
3.46 x 105 / 6.02 x 1023 = 5.75 x 10-19 J

(g) What is the minimum frequency of uv light is needed to break a C-Cl bond?
E = h x f, so f = E /h
The frequency required
= 5.75 x 10-19 / 6.63 x 10-34 = 8.67 x 1014 Hz

(h) What is the maximum wavelength of uv light capable of breaking a C-Cl bond?
c = w x f, w = c / f ,
wavelength to break C-Cl bond = 3.00 x 108 / 8.67 x 1014 = 3.46 x 10-7 m
= 3.46 x 10-7 x 109 = 346 nm [3sf]