electron behaves as wave because
In past it came to be known that light behaves both as a wave and as a stream of particles,depending upon the situtation...so then percieving to the symmetry of nature,Louis de Broglie suggested that 'particles' should also behave as a wave..and so according to his hypothesis it is not only electrons,,its me,you, a moving train etc, evry particle behave as wave.. Even Broglie proved Bohr's 2nd law using his hypothesis,which was previously experimentaly obtained... and so it is that an electron behaves as a wave...and we can even measure it...also it is interesting that we too have a wavelenght but our mass is so huge that it is quite neglegible..and so we behave a much as particles only..hopefully it is explained..
I think we cannot explain why it acts like a wave,it just acts like one, physics can only predict things,it cannot answer why it act like this,by the way ,I think we say an electron acts like a wave because if we use the "wave" model we can explain how it behave ,therefore we say it is a wave
wel in physics there are assumptions and models,,,whicheva suits the best,,is taken as the probable behaviour..and so i think we can explain an electron as a wave...because it suits and explain many observations which cannot be explained on its particle nature,,,which itself is another retriceumption or explanation..
In the studies it is known that the light has both partical nature and wave nature... similarly debrogli has connected the partical nature of an electron to a wave nature... and said that micro particals have wave nature...
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