Answer to Question #218944 in Statistics and Probability for wexie

Question

Consider the electron particle .The function F(r)=l-(2r²+r+l)e^-2r is the CDF of the distance r, of the electron in a hydrogen atom from centre of the atom. The distance is measured in Bohr radii where 1 Bohr radius=5.29*10^-11m. Calculate to two decimal places the value of F(l),and interpret its meaning.

Answer 1

$$F(r)=1-(2r^2+2r+1)e^{-2r}$$

Then

$$F(1)=1-(2(1)^2+2(1)+1)e^{-2(1)}=1-5e^{-2}\approx0.32$$

 $F(1)=0.32$ means that the electron is within 1 Bohr radius from the center of the atom 32% of the time.