Question

Radial component of the hydrogen-like wavefunctions (20 points total) 2. (10 pts) By considering the radial component of the 1s orbital of H atom, compute the most probable distance between electron and nucleus in the 1s state of H atom. (10 pts) With what probability the electron can be found anywhere farther than this most probable distance?

Answer 1

we know radial component R_{​​​​​​nl}​​​​(r) = 2 (z/a0)^3/2 e ^{-- z.r/a0} ------(1)

and most probable radius r_{​​​​​​mp}​​​​ = a0 = bohr radius for hydrogen = 0.529 angstroms.

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to take probability beyond the most probable radius we have to take limits a0 as lower limit and infinity as a upper limit.

P(r) = 5 e^{​​​​​​-2} = 0.6768 is probability beyond bohr radius

please find attached file for detailed information. put one like if satisfied...
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