Probability of finding an electron at a great distance from nucleus

[Arnav]

I recently learnt that according to quantum mechanics, the probability of finding an electron anywhere(except nodes) is non zero. The probability of finding the electron of the sodium atom in my vapour lamp, in Andromeda galaxy is, although very very small, but non zero.

I am unable to wrap my head around this fact. Is the aforesaid statement just a mathematical consequence? Could someone please explain this to me?

P.S. I am a high school student, so it would be extremely good if someone could explain this to me in layman terms

[swansont]

Yes, it’s a mathematical consequence, because the equation that describes the probability is math.

Quantum mechanics can be hard to conceptualize, as some ideas are at odds with classical, everyday notions. Such as the electron having some particle behaviors and some wave behaviors, and the way probability shows up in the way things work.

The hydrogen radial wave function drops off as e^-r/a (and probability is the square of that) so while there is a probability of finding the electron far from the nucleus it is vanishingly small.

[Arnav]

okay thanks for the answer swansont