# How does an atom's electric field overcome an electron's inertia?

An electron has mass, and therefore has inertia. How does an atom's electric field perpetually overcome an electron's inertia, necessary to hold it in its shell? Does this require continual work to be performed by an atom's electric field, and represent a conservation of energy violation? Do electron elemental and molecular bonds represent an energy violation in the same respect? Is the atom's field not performing work while it influences the motions of electrons?

I understand General Relativity proposes curved space to reconcile energy conservation laws in respect of overcoming an orbiting body's inertia by stating that gravity is not a force, but just objects traveling in straight lines through curved space. However there is no such proposition for the atom?

• Without invoking neither GR, nor QM, there is no violation of conservation laws, when a massive object (a star) keeps a planet in orbit, as the forces acting on the planet are roughly perpendicular to its velocity. Similarly, if you think of an atom as a classical object, an electron is roughly in a circular orbit with the Coulomb attraction acting perpendicular to its motion, thus performing no work. Of course, the electron is experiencing acceleration, which would suggest, that it ought to radiate EM waves, however quantization of allowed energy levels prevents that. Commented Feb 16, 2016 at 8:42

All spinning and orbiting objects overcome the inertia of their outer elements without continually doing work. Wheels, balls, planets, etc. They have to otherwise they would stop.

For example, if you have a ball and a piece of string and spin it around your head, the tension in the string (and the ball) provides a force that accelerates the ball inwards and overcomes (or rather redirects) its forward inertia.

Work is required to spin the ball up and create a tension in the string, but once moving it is not necessary to add additional energy to the system. The system is in balance. The ball is continually trying to move away from the string (maintaining tension) and the tension in the string is continually pulling it back.

Although the ball-and-string model is not a great analogy of electrons in orbit around a nucleus, the principle is the same in terms of how energy is conserved.

The "tension" between the electron and the nucleus is provided by the electromagnetic force (which indeed is also behind the tension in the piece of string).

The planetary model for an atom is a classical concept, and has many flaws, first noted by Rutherford. Bohr offered the first quantum fix, which was much improved by de Broglie.

Jumping ahead we have electron shells. The electrons exist as quantum probability waves, spread out throughout their shell. Calculation tells you the likelihood of a pointlike interaction with a specific electron, though wave interference effects must be included for accurate analysis.

• Thank you Peter. I am generally aware of modern proposed structure of atoms, electron probability waves/shells etc. The maths works, and so it must be that it represents something of reality. However I am not aware of the conversations which must have taken place, concerning implications for electron inertia. As electrons have mass, and how can a theory implicated with mass be disassociated with inertia? If this is so, then I would be very interested in the explanation, if it exists? Commented Feb 16, 2016 at 12:17