# What causes electron to orbit the nucleus in an atom? [closed]

What causes the electron to orbit the nucleus? Which is the force that causes it to do so? Is it related to the Electro - Magnetic force? .

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## closed as unclear what you're asking by Emilio Pisanty, Dan, Waffle's Crazy Peanut, Manishearth♦Aug 29 '13 at 11:58

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Hi Aparajita, please specify your doubt? What do you believe? Electrodynamics is a field, do you mean electrostatics coulomb force? If yes, then you are right, it is electrostatics coulomb force that provides necessary centripetal force to electron for circling around the nucleus. –  orion Aug 25 '13 at 13:36
I meant electrostatic force, I actually wanted to ask why do electrons move at all? What makes them move? –  APARAJITA Aug 25 '13 at 13:48
Consider this, an electron that is away from the positive nucleus (i.e. which is not part of the atom) gets attracted toward it due to electrostatics force. –  orion Aug 25 '13 at 13:59
Quantum physical rules does not allow it to fall inside nucleus and hence it starts orbiting around it. When it started orbiting in the nth orbit, it had the angular momentum $n\hbar$. It keeps on orbiting due to conservation of angular momentum. –  orion Aug 25 '13 at 14:07
Related: physics.stackexchange.com/q/9415/2451 and links therein. –  Qmechanic Aug 25 '13 at 15:39

I don't understand what you are asking here...

## If you're asking for why the electron actually accelerates due to it's revolution

It's a result of basic kinematics. When it's orbitting, it's direction is continuously changing, so the velocity (which incorporates the direction) must keep changing, therefore an accceleration; this acceleration is called the centripetal acceleration, given by:

$$a=\frac{v^2}r$$

This can easily be derived, if you know some very basic calculus and vector algebra. c.f. This Khan Academy video.

## If you're asking what keeps it in orbit around the nucleus

Well, this is hard to answer, because in reality, the electron doesn't exactly orbit.

In the Rutherford Model, the electromagnetic attraction between the (positive) nucleuss and the (negative) electron is what kept it in orbit. This electromagnetic force can be calculated through the Maxwell equations and the Lorentz force.

In the Bohr Model, again, it's the electromagnetic force; however, the energy levels of the electrons are quantised. It couldn't have any energy but they should be multiples of a particular energy, called the Rydberg energy. Specifically,

$$E=-\frac{Z^2}{n^2} R_E$$

And $R_E$ is given by:

$$R_E=\frac{({k_ee^2})^2m_e}{2\hbar^2}$$

In other words, the bohr model and old quantum theory is identical to the classical models except that all the classical motions are not allowed. The motion must satisfy the following rule, known as the Old Quantum Rule:

$$\int p\mbox{ d}q =n\hbar$$

In Modern Quantum Mechanics, however, the electron does not orbit the nucleus.

It is a standing wave (the wavefunction/state vector) around the nucleus; and it's energy levels are given by the Eigenvalues of the Hamiltonian:

$$E\psi = H\psi=i\hbar\frac{\partial\psi}{\partial t}$$

In QFT, again the same thing, the electron does not orbit; it's an excitation of the electron field determined by the Dirac Equation. The energy levels are given by:

$$E=\sqrt{1-\alpha^2Z^2 }$$

Where $\alpha\approx\frac1{137}$ is the fine structure constant. Which is why you can't have more than 137 electrons.

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I mean what makes them move at all –  APARAJITA Aug 25 '13 at 13:56
Why did you edit my question? My question is simple , why do the electrons move at all? –  APARAJITA Aug 25 '13 at 14:03
@APARAJITA: Because it was not clear that way, so I clarified it. I did answer the "what makes them move at all", in the secondf part. –  Dimensio1n0 Aug 25 '13 at 14:06
Thank you dimension10, you do know quite a lot –  APARAJITA Aug 25 '13 at 14:08