Levels of Bohr
Look at the units in the expression for the energy levels of the electrons in a hydrogen atom according to the Bohr model.
Age
16 to 18
Challenge level
Problem
The energy levels of the electrons in a hydrogen atom according to the Bohr model are given by
$$
E_n = -\frac{m_ee^4}{8\epsilon_0^2h^2n^2}\, n=1, 2, 3, \dots
$$
where $m_e$ and $e$ are the mass and charge of the electron, $h$ is Planck's constant and $\epsilon_0$ the permittivity of free space.
This expression draws together many the fundamental constants involved in quantum mechanics. What are all of the S.I. units of these constants?
Using just these constants is it possible to create a dimensionless quantity?
Can you make a quantity with dimensions $[L]$ (length) or $[T]$ (time) using these quantities?