A challenge to understanding electrons in atoms is that they are governed by the laws of quantum mechanics rather than the Newtonian laws that govern the physical world we interact with on a regular basis. One particular peculiarity is that we can no longer think about "particles". It would be nice if an atom were like the little picture that we all have of an electron orbiting a nucleus like the planets orbit the sun. However comforting this picture is (and we will often fall back on this picture as we try to "visualize" and draw atoms), it is not correct. There are many reasons for this but one of the most glaring is that we cannot think of electrons as particles that are localized in space. They are instead strange quantum mechanical beasts that at times appear to be particles and at other times seem to behave like waves. This wave particle duality is often discussed in terms of electrons being both waves and particles. It is better to remember that electrons are neither waves nor particles (as both of these are classical ideas) but instead are some new strange thing that only appears to us as being wave-like or particle-like depending on how we are interpreting different experiments.
This wave particle duality exists in other situations such as electro-magnetic radiation. We nearly always deal with EM radiation as a wave. However, the photoelectric experiments showed that the energy of light interacting with electrons requires us to take the new perspective that the energy appears to come from particle-like objects as it is proportional to the frequency of the light. This is why we invent the notion of a "photon" or packet of light. The "photon" is our idea of a light particle.
Because electrons (and other very low mass "particles") are quantum mechanical, they don't behave as we would expect from classical mechanics. One of the key manifestations of this is the fact that we can either know the precise location of a particle but not its momentum. Or we can know its momentum exactly but have no idea about its location! Just let that sink in for a moment. If it sounds strange (even impossible), it should. This is not the way the world around us appears. A baseball has a location and velocity. You know where it is. You know where it is going. This is not the case with quantum mechanical objects such as an electron. You might know something about its location, and something about where it is going. But you don't get to know both of these precisely. This idea is referred to as the Heisenberg uncertainty principle that states there is a minimum product of the uncertainties of position and momentum.
\[\Delta x \Delta p \geq { h \over 4 \pi } \]
Where \(\Delta x\) is the uncertainty in position (how well do you know the position). And \(\Delta p\) is the uncertainty in momentum (how well do you know the momentum or "where it is going"). If you knew the exact position of an electron then \(\Delta x\ = 0\) as you know it exactly. If you knew it to about 1 nm, then \(\Delta x = 1 nm\). The product of these two uncertainties must be not only finite but greater than \( {h / 4 \pi}\). Luckily, Planck's constant, \(h\), is a very, very small number. Thus we can know quite a bit about the location and momentum; we just can't know them exactly. Is this true for everything? Technically it would apply to everything not just systems we dubbed as quantum mechanical. However, since \(h\) is so small the only times these uncertainties are relevant is when we are interested in very small distances (like distances in atoms and molecules) and when we are interested in very small momentums (like those for particles with small masses like an electron).
How then do we deal with these small particles that are governed by different rules? We have to come up with a new model to explain their behavior since Newton's laws will fail us. The new model that we will use is Quantum Mechanics.