The energy required to separate an a hydrogen atom in to electron and proton is 13.6 ev. Compute the orbital radius and velocity of electron in hydrogen atom.
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Answer:
2.19 * 10^6 m/s
Explanation:
Equating the Coulomb force to the generic expression for the centripetal force we have,
1
4
π
ϵ
0
e
2
r
2
=
m
v
2
r
This gives the kinetic energy as,
T
=
1
2
m
v
2
=
1
8
π
ϵ
0
e
2
r
−
−
−
−
−
−
−
(
1
)
The Coulomb interaction potential energy is,
V
=
−
1
4
π
ϵ
0
e
2
r
−
−
−
−
−
−
−
−
−
−
(
2
)
Adding (1) and (2) we get the total energy as,
E
=
−
1
8
π
ϵ
0
e
2
r
−
−
−
−
−
−
−
−
−
(
3
)
This is given to be
−
13.6
e
V
.
Equating we get,
1
8
π
ϵ
0
e
2
r
=
13.6
×
1.6
×
10
−
19
−
−
−
−
−
−
−
−
−
−
(
4
)
Now the electronic charge
e
=
1.6
×
10
−
19
C
And,
1
4
π
ϵ
0
=
9
×
10
9
S
I
u
n
i
t
s
Substituting these values in (4) we get,
r
=
0.53
×
10
−
10
m
.
Also from (1) we have,
v
=
√
1
4
π
ϵ
0
e
2
m
r
−
−
−
−
−
−
(
5
)
The electron mass is
m
=
9.1
×
10
−
31
k
g
Substituting the value of m as above and the value of
r
=
0.53
×
10
−
10
m
in (5) we get,
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