Question

In a one electron system, the probability of finding the electron within a shell of thickness δr at a radius of r from the nucleus is given by the radial distribution function, P(r)=r2R2(r).

An electron in a 1s hydrogen orbital has the radial wavefunction R(r) given by

R(r)=2(1a0)3/2e−r/a0

where a0 is the Bohr radius (52.9 pm).

Calculate the probability of finding the electron in a sphere of radius 1.9a0 centered at the nucleus.

In a one electron system, the probability of finding the electron within a shell of thickness or at a radius of r from the nucleus is given by the radial distribution function, P(r) = rR(r). An electron in a 1s hydrogen orbital has the radial wavefunction R(r) given by R(r) = 21 - 13/2 - e-rla where do is the Bohr radius (52.9 pm). Calculate the probability of finding the electron in a sphere of radius 1.9ao centered at the nucleus. probability:

Answer 1

$Radial\ probability = P(r)4\pi r^{2}dr$

$\int_{0}^{1.9*52.9*10^{-12}}4*\pi *r^{4}*4*\frac{1}{(52.9*10^{-12})^{3}}*e^{-\frac{2r}{52.9*10^{-12}}}dr = 3.5*10^{-20}$