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Answer» Answer:
f
=
8.225
×
10
14
l
Hz
Explanation:
The Balmer SERIES corresponds to all electron transitions from a higher ENERGY LEVEL to
n
=
2
.
eilat.sci.brooklyn.cuny.edu
eilat.sci.brooklyn.cuny.edu
The wavelength is given by the Rydberg formula
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
∣
∣
∣
∣
a
a
1
λ
=
R
(
1
n
2
1
−
1
n
2
2
)
a
a
∣
∣
∣
∣
−−−−−−−−−−−−−−−−−−−−−−−
where
R
=
the Rydberg constant and
n
1
and
n
2
are the energy levels such that
n
2
>
n
1
Since
f
λ
=
c
we can re-write the equation as
1
λ
=
f
c
=
R
(
1
n
2
1
−
1
n
2
2
)
or
f
=
c
R
(
1
n
2
1
−
1
n
2
2
)
=
R
′
(
1
n
2
1
−
1
n
2
2
)
where
R
′
is the Rydberg constant expressed in energy units (
3.290
×
10
15
l
Hz
).
In this PROBLEM,
n
1
=
2
, and the FREQUENCY of the limiting line is reached
as
n
→
∞
.
Thus,
f
=
lim
n
→
∞
R
′
(
1
4
−
1
n
2
2
)
=
R
′
(
0.25
−
0
)
=
0.25
R
′
=
0.25
×
3.290
×
10
15
l
Hz
=
8.225
×
10
14
l
Hz
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