Question

graph of probability of finding the 1s electron of hydrogen vs distance from the nucleus​

Answer 1

The hydrogen ground-state wave function is:

ψ(r)=1π−−√a3/20e−r/a0

Since the ground state is spherically symmetric, the probability of finding the electron in a thin spherical shell element dV is just the square of the wave function (i.e. the probability density) multiplied by dV:

|ψ(r)|2dV=[1πa30e−2r/a0]4πr2dr

To get the probability from zero to the Bohr radius, just integrate the probability over that region:

∫0a04a30e−2r/a0r2dr

which you can solve using integration by parts, or by just plugging it into Wolfram Alpha.

Answer 2

Answer:

Hope it will help you ☺️.