I didn't find any SE site for "Philosophy of Science" hence I am asking it on Physics SE because it is related to Physics more than to Philosophy. As law of gravitation is a model which was proposed by Sir I. Newton which explains many phenomenon but it fails to explain Mercury's trajectory around sun(and many other phenomenon also) so Einstein proposed his model of gravity. Now my question is: Is electron "Real" or just a Model? (Here by Real I mean can I observe it by any means). If someday we encounter a phenomenon which can't be explained by electron then, as we did in case of gravity, will we make another model to explain that phenomenon?
I don't think physicists find it worthwhile to ask this question. If you had a model that explained every known physical phenomenon, then there would be no way to test if it were "real" or only a model. If a question is not testable, then it is not a question science can answer.
If you look at a CRT type screen, the glow is caused by electrons hitting the phosphors and making them glow. Sounds pretty real to me. The electrons are being fired off the cathode, flying through the vacuum in the tube and hitting the back of the screen. They are tiny, but they are real.
I can see why you ask this question. I always struggle with the probabilistic interpretation of quantum mechanics and often find myself asking "is this REALLY what is happening, or, is this just a good model and description of processes?". But that doesn't mean to say that it is a good question. I don't mean this in a derogatory way (I emphasises this as this particular SE is guilty have having a certain amount of arrogance streaking through it), it's certainly an interesting question.
The problem with it is that it has no scientific meaning, also where do you stop with this line of thought? Is an atom 'real'? Are we real? Everything in physics is a model of some kind, models describing behavior always hold in a certain regime -- and then they break or deviate outside this regime.
A better question in my view, is "is the phonemenan commonly described as an electron real?" in which case the answer is yes!! Electrons are most deffinetly objects that can make themselves and their effects known. Your stipulation observed by any means is unfair. One can't observe the moons of saturn with the naked eye, but you can with a telescope. It also depends what you mean by observe. You can observe the flow of electrons in an electrical circuit -- current! You can't resolve an image of an electron as it is a point-like (so far as we know) particle.
You need to think more about what your question is really asking, and what answers can be attached to it. But despite the somewhat cold responses, I think your question is interesting even if not especially useful.
This is a very common philosophical question and there are various ways to answer it.
One useful way is the following: "Can you describe any experiment or observation where the reality (or lack thereof) of an electron would make any difference ?"
If you can't, then the whole question is meaningless. If there is no difference between the electron being "real" or being "a model" why bother asking the question?
This all, of course, goes back to that you need define "reality". If you can't create an operational definition that helps you to distinguish between real and not-real things, reality is just a pointless word. However, if you CAN create a definition, then you simply apply this to the electron and see what you get.