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Use the data from Figure 40.24 to calculate the first three vibrational energy levels of a C=Ocarbon-oxygen double bond.

Short Answer

Expert verified

Energy of n=1state = 0.107eV

Energy of n=2state=0.321eV

Energy ofn=3state=0.535eV

Step by step solution

01

Step 1. Given information

Energy level of harmonic quantum oscillator,

En=n-12h2

Here,

n denotes the state,

h = Planck's constant and

=classical angular frequency.

En=n-12h(2f)2

=n-12hf

=n-12hc

02

Step 2. Energy of n=1 state

E1=1-12hc

=hc2

E1=6.6310-34Js3.0108m/s2(5.8m)

=6.6310-34Js3.0108m/s2(5.8m)10-6m1.0m1.0eV1.610-19J

=0.107eV

03

Step 2. Energy of n=2 state

E2=2-12hc

=3hc2

E2=36.6310-34Js3.0108m/s2(5.8m)

=36.6310-34Js3.0108m/s2(5.8m)10-6m1.0m1.0eV1.610-19J

=0.321eV

04

Step 3. Energy of n=3 state

E3=3-12hc

=5hc2

E3=56.6310-34Js3.0108m/s2(5.8m)

=56.6310-34Js3.0108m/s2(5.8m)10-6m1.0m1.0eV1.610-19J

=0.535eV

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