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UPSEE 2018 Solved Paper
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© examsnet.com
Question : 38
Total: 150
For sodium light, the two yellow lines occur at
λ
1
and
λ
2
wavelengths. If the mean of these two is
6000
Å
and
|
λ
2
−
λ
1
|
=
6
Å
, then the approximate energy difference between the two levels corresponding to
λ
1
and
λ
2
is
2
×
10
−
3
e
V
2
e
V
2000
e
V
2
×
10
−
6
e
V
Validate
Solution:
Given, mean of
λ
1
and
λ
2
=
6000
Å
|
λ
2
−
λ
1
|
=
6
Å
i.e.
λ
1
+
λ
2
2
=
6000
Å
λ
1
+
λ
2
=
12000
Å
......(i)
λ
2
−
λ
1
=
6
Å
......(i)
Equating Eqs. (i) and (ii), we get
2
λ
1
=
12006
λ
2
=
12006
2
=
6003
Å
and
λ
1
=
5997
Å
Now, the energy difference is
Δ
E
=
h
c
λ
1
−
h
c
λ
2
Δ
E
=
h
c
(
1
λ
1
−
1
λ
2
)
Δ
E
=
6.6
×
10
−
34
×
3
×
10
8
×
(
λ
2
−
λ
1
λ
1
λ
2
)
=
6.6
×
10
−
34
×
3
×
10
8
×
6
×
10
−
10
5997
×
10
−
10
×
6003
×
10
−
10
×
1.6
×
10
−
19
e
V
=
2.12
×
10
−
3
e
V
≃
2
×
10
−
3
e
V
© examsnet.com
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