For 1s orbital Hydrogen atom radial wave function is given as: R(r) =1/(sqrtpi) ((1)/(a_0))^(3//2) e^(-r//a_0) (where a_0 = 0.529 A^@) .The ratio of radial probability density of finding electron at r = a_0 to the radial probability density of finding electron at the nucleus is given as (x.e^(-y)). Calculate the value of (x + y).

For 1s orbital Hydrogen atom radial wave function is given as: R(r) =1

1.	For 1s orbital Hydrogen atom radial wave function is given as: R(r) =1/(sqrtpi) ((1)/(a_0))^(3//2) e^(-r//a_0) (where a_0 = 0.529 A^@) .The ratio of radial probability density of finding electron at r = a_0 to the radial probability density of finding electron at the nucleus is given as (x.e^(-y)). Calculate the value of (x + y).
Answer» Solution :`[(R(r)]^2 r=0)/([R(r)]^2 "atnucles")= ([1/(sqrt(PI))(1/(a_0))^(3/2) ][e^((r)/(a_0))]^2)/([1/(sqrtpi) (1/(a_0))^(3/2)]^2 [e^((r)/(a_0))]^2 )= e^(-2)` r=0`therefore x + y =3`