Answer to Question #218944 in Statistics and Probability for wexie

Question #218944

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.


1
Expert's answer
2021-07-26T11:10:54-0400
F(r)=1(2r2+2r+1)e2rF(r)=1-(2r^2+2r+1)e^{-2r}

Then


F(1)=1(2(1)2+2(1)+1)e2(1)=15e20.32F(1)=1-(2(1)^2+2(1)+1)e^{-2(1)}=1-5e^{-2}\approx0.32

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



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