WEBVTT
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This is College Physics Answers
with Shaun Dychko.
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A lithium-bromide molecule
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oscillates with a frequency of 1.7 times
10 to the 13 hertz
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and our questions are -
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what is the energy difference between
oscillator states?
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And then given that the oscillator has an
energy of 1 electron volt in part (b),
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figure out which state that must be,
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what is the number, n, in other words?
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So we are told by equation [29.3]
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that the difference in
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consecutive energy states is
Planck's constant
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times the frequency of the oscillation.
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So that's 4.14 times 10 to the minus
15 electron volt seconds
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times 1.7 times 10 to the 13 hertz,
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which gives an energy difference between
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states of 0.070 electron volts.
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And we chose this value for Planck's
constant because we wanted
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to have our answer in electron volt units.
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Now in part (b), we have to
figure out, what is
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*n* in this formula, this is [29.1].
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And we'll solve it for *n*
by first multiplying
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through by *hf* into the brackets
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and so we have *nhf* plus
one-half times *hf*
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equals the energy
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and we'll switch the sides around to
have the unknown—*n*—on the left.
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Then subtract *hf* over 2 from both sides
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and you get this line here
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and then divide both sides by Planck's
constant times frequency
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and you end up with this line here.
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These *hf*'s cancel there leaving *hf*
in the denominator below energy.
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So the *n*th state is energy
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divided by Planck's constant times
frequency minus a half.
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So that's 1 electron volt
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divided by Planck's constant, using
electron volt units,
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in order to match with the electron volt
units in the numerator.
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And multiply by the frequency
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minus a half gives us 13.7 and the closest
whole number to that is 14;
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*n* has to be a whole number,
which is to say it can be 1
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0, 1, 2, 3, and so on.