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KVPY SX SB Exam 2015 Question Paper
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© examsnet.com
Question : 33
Total: 120
A donor atom in a semiconductor has a loosely bound electron. The orbit of this electron is considerably affected by the semiconductor material but behaves in many ways like an electron orbiting a hydrogen nucleus. Given that the electron has an effective mass of 0.07 m
e
, (where me is mass of the free electron) and the space in which it moves has a permittivity 13
ε
0
, then the radius of the electron's lowermost energy orbit will be close to (The Bohr radius of the hydrogen atom is 0.53 Å)
0.53 Å
243 Å
10 Å
100 Å
Validate
Solution:
From Bohr postulates
k
z
e
2
r
2
=
m
v
2
r
….(i)
m
v
r
=
n
h
2
π
….(ii)
⇒
v
=
e
2
2
ε
0
h
z
n
r
=
n
h
2
π
m
v
r
=
n
h
2
π
m
(
e
2
2
ε
0
h
)
(
z
n
)
r
=
(
ε
0
h
2
π
m
e
2
)
(
n
2
z
)
r
=
r
0
n
2
z
Because the medium of permittivity
ε
=
13
ε
0
effective mass m = 0.07 m
e
r
=
13
r
0
0.07
n
2
z
At ground state (n = 1, assuming like H atom, z = 1)
r
=
13
0.07
(
0.53
Å
⇒
r
≈
100
Å
© examsnet.com
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