# Uniform circular motion of electrons?

Can we use the uniform circular motion formulae to calculate the velocity of an electron along with the formula of radius of nth Bohr orbit? And using that can we calculate the kinetic energy of an electron?

## 1 Answer

Well yes you can if you assume the Bohr model is correct. However in reality, it is a little bit more complicated than that. In reality everything have both particle and wave like properties, which builds the foundation of quantum mechanics. The lighter the object, the more wave like properties it exhibits and the heavier the object, the more particle like properties it exhibits. So a ball actually has wave light properties but it is too heavy for it to be notices. Meanwhile a light wave actually has particle properties, however it is too light to be noticed. Electrons on the other hand turn out to a mass between these two extremes, hence both its particle and wave like properties are able to be noticed.Hence it is important to stop thinking electrons as small point particles.

Another important concept is the Heisenberg Uncertainty Principle which is the following formula: $$\Delta x \Delta p \geq \hbar$$ This means that the uncertainty of an object's position multiplied by the uncertainity in an object's momentum at best can only be equal to the constant value: $\hbar$ which equals $1.054*10^{-31}$ This equation can be applied to electrons. Hence, the important thing that this equation tells us about electrons in an atom is that rather electrons moving in a predictable circular orbit, they actually travel in any path that they want and we actually can't precisely determine position of the electron in an atom. Hence the quantum mechanical model of the atom actually consists of orbitals, rather than orbits.

Orbitals is the area which an electron is in 90% of the time. There are 4 main type of oribitals, s, p, d and f shown below. So, finding the velocity of an electron is little more complicated than using simple classical mechanic equations. However its velocity can be determined in simplified conditions using quantum mechanics.