Thus, for a  dynamically stable orbit in a
hydrogen atom
    Fe = Fc
2
2
2
0
1
4 ε
=
π
e
mv
r
r
(12 2)
Rationalised 2023-24
Physics
296
Thus the relation between the orbit radius and the electron
velocity is
2
2
0
4
e
r
εmv
=
π
(12 3)
The kinetic energy (K) and electrostatic potential energy (U) of the electron
in hydrogen atom are
2
2
2
0
0
1
 and 
2
8
4
e
e
K
mv
U
r
r
ε
ε
=
=
= −
π
π
(The negative sign in U signifies that the electrostatic force is in the –r
direction ) Thus the total energy E of the electron in a hydrogen atom is
2
2
0
0
8
4
e
e
E
K
U
r
r
ε
ε
=
+
=
−
π
π
                 
2
0
8
e
εr
= −
π
(12