Wave-particle duality in electron
Interesting question and this is a complicated topic. Actually it is not true that the wave and particle models are each valid 50 percent of the time. I think it is better to say that the wave model is always valid, but under some conditions the wave gets compressed down to a small area, so it looks like a particle. I hope that makes sense, please comment if it doesn't?

I am not a quantum chemist, but I think the normal conditions for electrons in atoms and molecules are not ones that make them act like particle. So therefore we should always think of them as waves. Luckily we can still talk about the "inner" and "outer" electrons while they are waves. It is not "inner" and "outer" exact position, it is an area occupied by the wave, the "inner" one is nearer to the nucleus, the "outer" one if further away. For atoms these are called atomic orbitals - if you look them up on Wikipedia it might be very interesting.

If you want to solve the energy, wavelength and position, it's quite complicated. I would recommend studying quantum mechanics. It will take a long time to get there, although it is very interesting. There might be a quicker but less detailed course just for chemists to do these calculation too. I hope that's helpful.