# Finding the wavelength of an electron in its ground state?

To find the wavelength of an electron in its ground state in a hydrogen atom, would I or could I do the following?

1. Use the ground state energy (-13.6eV) in $E^2 = m^2c^4 + p^2c^2$
2. Solve for $p$
3. Use $p$ to find $λ$ in $λ = h/p$

Also, if I wanted to find the total energy of an electron in another state given the wavelength, could I just do the above process backwards (use $λ$ to get $p$, then find $E$)?

Let me know if I'm simply completely incorrect, missing a step, or if there's anything wrong here please.

• Seems good to me. Make sure your units are correct. eV can be pesky, so convert everything into Joules. A little trick I learned in undergrad was that if I have everything in MKS (meters kilograms and seconds,and my constants in those units) then you wont have unit problems EVER! Ya its annoying to use $\hbar$ in $10^{-34}$ J$\cdot$s but $10^{-15}$ eV isn't much better. – John M Apr 24 '13 at 2:21
• The electron in an H atom isn't a plane wave or any superposition of plane waves, so it isn't clear what wavelength means in this context. I suppose if you approximate the potential by a harmonic potential you could calculate the wavelength for the corresponding harmonic oscillator ground state. – John Rennie Apr 24 '13 at 9:38

• Given an average radius of the ground state ($5.29*10^-11m$) could I use the aforementioned method? Moreover, you mentioned finding the uncertainty in position - would $ΔxΔP = h/4π$ be of use here somehow? – Stumbleine75 Apr 24 '13 at 3:30