Why is the velocity of electrons greater in first orbit despite the fact that it has least energy in first orbit?
When considering why a particle behaves the way it does as it orbits another body, two things must be considered: the force of attraction between the two particles, and the speed at which the particle orbits. If the particle is closer to the nucleus of the atom, it must travel faster to counteract the increase in the force of attraction between it and the particles in the nucleus. Here's an interesting example that will illustrate this concept. Get a whistle on a lanyard, or a pendant necklace, something that basically has a length of string with a weight at the end of it. Twirl the length of string, letting the string wind on your fingers. You will notice the weight of the pendulum goes faster as the string gets progressively shorter. This is why the electrons in the lowest energy level go the fastest, because they will be pulled in by the force of the nucleus attraction otherwise.