Is the velocity of electrons in different energy shells same or different? want to understand concept of angular momentum and velocity of electrons in different shells along with their interaction to nuclear force 
 A: The electrons interact to first order only electromagnetically and weakly, so the only measurable interaction for an electron   is the electromagnetic one in the field generated by the protons of the nucleus combined with the field of the rest of the electrons. The simplest example is the hydrogen atom, where just using the coulomb potential all the observed energy levels can be fitted.
The solutions are quantum mechanical, and an estimate of the velocity can be made from the angular momentum of the state occupied by the electron, which angular momentum L 
$L^2=l(l+1)(h/2π)^2$
$l$ is the angular momentum quantum number which runs from zero up to the  $n-1$, where  $n$ is the principle quantum number and shells being defined by the $n$ quantum number
One then can go to the semiclassical  Bohr model, and use the classical definition of angular momentum:
Where $L=mvr$ and get the velocity. The higher the $n$ the higher $l$ can go, so higher shells may give higher velocities although even for $l=0$ there exists an orbital going through the center of the potential for all n, where the use of angular momentum for velocity estimate fails.
The Bohr model is not such a bad approximation to the quantum mechanical orbitals.
