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BeO Vibrational Transitions.pdf
1. 1
The vibrational
transition in BeO
is observed at a
wavelength of
6.724 μm. What
is the effective
force constant of
BeO?
Helping Tools
No.1
No.2
2. 2
No.3
Solution
1 2
1 2
2
Let us first calculate the
reduced mass of BeO as
(9.0122 )(15.9994)
(9.0122 ) (15.9994)
144.19
5.76
25.01
r
m m
m
m m
u
u
u
u
u
=
+
=
+
= =
3. 3
8
6
14 1
12
We know that frequency
& wavelength are related by
3 10
6.724 10
0.446 10
44.6 10
m
X
c s
f
X m
X Xs
X Hz
−
−
= =
=
=
2
2
2
2
2 2
We know that vibrational
frequency is given as:
1 1
2 2
1
4
k kXc
f
m mXc
kc
f X
mc
= =
=
2 2 2
2
12 2 2
2
24 2
2
16
2
24 6
16 2
30
16 2
14 18
2
4
(44.6 10 ) 4 (3.14) 5.76 931.5
1989.16 10 ( ) 39.44 5365.44
9 10
420932022.78 10 10
9 10
420932022.78 10
9 10
46770224.75 10 4677.022475 10
f X Xmc
k
c
X Hz X X X X MeV
c
X Hz X X MeV
m
X
s
X X eV
X m
X eV
X m
X eV X e
m
=
=
=
=
=
= = 2
21 3
2 2
4.677 10 4.677 10
( )
V
m
eV eV
X X
m nm
= =
