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we know that every Isolated atoms are spherically symmetric.how we know its shape, is there is any membrane covers it as skin of our body?

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There is no membrane, no skin, and moreover, no shape and no body. If you ever think of applying any of these words to an atom, then you have a major misconception about the nature of atoms and elementary particles.

An isolated atom is spherically symmetrical in that it reacts the same way no matter which side you approach it from. As for the actual picture of an atom, take a photo of a streetlight in a thick fog from far away, or be content with the image from Wikipedia.

Kinda atom

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There is no membrane. In principle the electron could be at a very large distance from the nucleus, but the probability decreases fairly quickly as a function of distance.

Edit:

Technically, you could create a boundary surface diagram that draws a "surface" around the atom that represents some cutoff for the probability. Of course, it doesn't mean much because the electron can go right through it. For an atom, this is just spherical, but it is certainly more interesting if you have a molecule.

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