Assume the Bohr model to determine the radius of the n = 8 orbit in a N 6+ ion.
ID: 980311 • Letter: A
Question
Assume the Bohr model to determine the radius of the n = 8 orbit in a N6+ ion.
r = ? pm
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What is the energy in joules of a photon with a frequency of 7.95e+14 s-1? What is the energy in kilojoules of a mole of photons of this frequency? Express you answers to three significant digits.
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Be carefull of the sign of your answers and express your numerical answers to four figures.
E of single photon = ? J E of mole of photons = ? kJ/molExplanation / Answer
(1) r = 53 X n2/Z pm
r = 53 X 64/7 pm
r = 484.57 pm
(2)
E = h X frequency
E = 6.626 X 10-34 X 7.95 X 1014
E = 5.27 X 10 -19 J
For 1 mole, E = 6.023 X 1023 X 5.27 X 10-19 = 317.4 kJ/mol
(a) E = - 13.6 / n2 eV = -13.6 X 1.602 X 10-19 / 52 J = - 8.71 X 10 -20 J
(b) E = -13.6 X 1.602 X 10-19 / 92 J = - 2.69 X 10 -20 J
(c) delta E = E9 - E5 = - 2.69 X 10 -20 - (- 8.71 X 10 -20 ) = 6.02 X 10 -20 J