state the postulates of bohrs model and derive the expresion for the energy of an electron in the atom
Answers
Answer:Postulates of Bohr's Model of an atom: ... In an atom, electrons(negatively charged) revolve around the positively charged nucleus in a definite circular path called as orbits or shells. 2. Each orbit or shell has a fixed energy and these circular orbits are known as orbital shells.
According to Rutherford's model, we have
r
mv
2
=
4πϵ
0
1
r
2
Ze
2
⟹ =
4πϵ
0
1
r
Ze
2
Therefore,
Total Energy =P.E+K.E
T.E=−
4πϵ
0
1
r
Ze
2
+
2
1
mv
2
=
2
1
4πϵ
0
1
r
Ze
2
=−
8πϵ
0
1
r
Ze
2
Energy is negative implies that the electron- nucleus is a bound or attractive system.
OR
According to Bohr's atomic model, electrons revolve around the nucleus only in those orbits for which the angular momentum is an integral multiple of
2π
h
So, as per Bohr's postulate, we have
mvr=
2π
nh
Therefore,
r
mv
2
=
4πϵ
0
1
r
2
Ze
2
mvr=
2π
nh
Therefore,
m
2
v
2
r
2
=
4π
2
n
2
h
2
This implies,
r=
πZe
2
m
ϵ
0
n
2
h
2
This is the required expression for Bohr's radius.
Explanation: