Lecture 2
Dual Nature of Light
wave
λν= c
λ= wavelength
ν = frequency of light
c = speed of light = 3.00 ×108
E = hν = Energy of a photon
h = Planck’s constant = 6.63x10−34Js
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Sample Problem
Visible radiation of wavelength 610 nm is emitted when lithium is excited by flame or
electric discharge. Calculate the frequency for radiation with a wavelength of 610 nm.
Calculate the energy of a photon when the wavelength is 610 nm
Summer 2005
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Chem 6 Study Guide
Lecture 2
Bohr Model of H atom
Energies of the allowed states of H atom are:
⎛ 1⎞
E n = − RH ⎜ 2 ⎟
⎝n ⎠
n = 1, 2, 3, ….. principal quantum number
RH = Rydberg constant = 2.18x10−18J
Atoms absorb or emit light when e− changes its orbit
or
∆E = E f − Ei = hν
⎛ 1
1 ⎞
hν = ∆E = RH ⎜⎜ 2 − 2 ⎟⎟
⎝ ni n f ⎠
where ni and nf are integers.
This predicts the H-atom spectrum EXACTLY!
nf > ni
∆E is +
(absorbs photon)
∆E is −
(emits photon)
nf < ni
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Note:
Sample Problem
When an electron in the hydrogen atom changes from n = 5 to n = 1, what is the
energy of the photon involved?
Is a photon emitted or absorbed?
Summer 2005
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Chem 6 Study Guide
Group Problems
Light and the Bohr Model
1.
Name ____________________
A quantum of electromagnetic radiation has a wavelength equal to 7.52 × 106 Å. What is the
frequency of this radiation in cycles/sec?
(a) 1.13 × 10−12
(b) 8.80 × 10−26
(c) 3.99 × 10+11
(d) 9.45 × 10+13
(e) 2.69 × 10−15
HINTS
Convert the wavelength in Å to meters.
Be sure to include units and show how they cancel in the process of solving the problem.
2
Calculate the energy in joules of 1 mole of 675 nm photons.
(a)
(b)
(c)
(d)
(e)
3.
What is the wavelength of the radiation when an electron in the Hydrogen atom goes from n= 5 to
n=1 level? (Use the information about the energy of the photon (demonstration problem) to
calculate the wavelength.)
(a)
(b)
(c)
(d)
(e)
4.
2.25 x 10−15J
2.94 x 10−19J
1.99 x 10−25J
1.77 x 105J
675J
91 nm
114 nm
95 nm
456 nm
2280 nm
When an electron changes from n = 6 to n = 2, is the energy change greater than or less than the
energy change that occurs when the electron goes from n = 5 to n = 1? (Can you answer this
without actually calculating the energy change?)
Summer 2005
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Chem 6 Study Guide