For the hydrogen state,

PHYSICS · Subjective · Fermi University Physics · Atomic, Molecular & Optical Physics · One-electron atoms and the origins of atomic structure · One-electron atoms and the origins of atomic structure

Reading the Spectrum, Ch Radial functions, orbital size and Rydberg states

Problem

For the hydrogen 1s1s state, P(r)=4a03r2e−2r/a0P(r)=\dfrac{4}{a_0^3}r^2e^{-2r/a_0}. Using ∫0Rr2e−br dr=2b3−e−bR(R2b+2Rb2+2b3)\int_0^R r^2e^{-br}\,dr=\dfrac{2}{b^3}-e^{-bR}\left(\dfrac{R^2}{b}+\dfrac{2R}{b^2}+\dfrac{2}{b^3}\right), calculate the probability that the electron is found within one Bohr radius of the nucleus, i.e. at r<a0r<a_0.

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