Using Rutherford model of the atom, derive the expression for the total energy of the electron in hydrogen atom. What is the significance of total negative energy possessed by the electron?
OR
Using Bohr's postulates of the atomic model derive the expression for radius of nth electron orbit. Hence obtain the expression for Bohrs radius.
According to Rutherford's model, we have
mv2r=14πϵ0Ze2r2
⟹ =14πϵ0Ze2r
Therefore,
Total Energy =P.E+K.E
T.E=−14πϵ0Ze2r+12mv2
=1214πϵ0Ze2r
=−18πϵ0Ze2r
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 h2π
So, as per Bohr's postulate, we have
mvr=nh2π
Therefore,
mv2r=14πϵ0Ze2r2
mvr=nh2π
Therefore,
m2v2r2=n2h24π2
This implies,
r=ϵ0n2h2πZe2m
This is the required expression for Bohr's radius.