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Byju's Answer
Standard XII
Physics
Validating the Bohr's Model
An electron i...
Question
An electron in an excited state of
L
i
2
+
ion has angular momentum
3
h
2
π
. The de Broglie wavelength of the electron in this state in
p
π
α
0
(where
α
0
is the Bohr radius). The value of
p
is
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Solution
Angular momentum,
L
=
n
h
2
π
=
3
h
2
π
⇒
n
=
3
Also, Wavelength
λ
=
h
p
=
h
r
m
v
r
=
h
r
3
h
2
π
=
2
π
r
3
...(1)
But,
r
=
a
0
n
2
Z
....(2)
Substituting (2) in (1),
λ
=
2
π
3
a
0
n
2
Z
=
2
π
3
a
0
3
2
3
=
2
π
a
0
⇒
p
=
2
comparing with the given expression
p
π
a
0
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