No. In essence, a correct model of electron orbitals does not have fixed velocity levels for different energy levels.
The simplistic Bohr model approximation derives a velocity of 2.188 x 10^6 meters per second or 2188 km/sec. This speed is about 150 times smaller than the speed of light in free space. For additional discussion and explanation of the probabilistic model, see the following reference:
Although it is convenient to think of the electron moving around the nucleus along circular paths, the correct description is a quantum mechanical one. This is tough to visualize, and hence people have stuck to the flawed picture of electrons moving along orbits.
In the more accurate quantum picture, the motion of the electron is described by probability functions and there is no fixed orbit. Different paths have different probabilities, and one can calculate average energy levels. These energy levels turn out to have exactly the same values as the energy levels calculated using the orbital (Bohr) model. However, the probability picture avoids the problem of an orbiting object losing energy through radiation.
For more information, you can search the Internet for the key phrase "Bohr Model." For example:: http://csep10.phys.utk.edu/astr162/lect/light/bohr.html
Answer partially provided by “Kurt” at http://www.fnal.gov/pub/science/inquiring/questions/electron_nucleus.html – retrieved 2016-04-18.