For `1s` orbital of Hydrogen atom radial wave function is given as :
`R(r)=(1)/sqrt(pi)((1)/(a_(o)))^(3//2)e^(-r//a_(o))` `(where a_(o )=0.529Å)`

The schrodinger wave equation for hydrogen atom is Psi_2 = (1)/(4sqrt(2pi))((1)/(a_0))^(3//2) (2-(r)/(a_0))e^(-r//a_0) where a_0 is Bohr.s radius. If the radial node in 2s be at r_0 would be equal to

The radial distribution function [P(r)] is use to determine the most probable radius, which is used to find the electron in a given orbital (dP(r))/(dr) for 1s-orbital of hydrogen like atom having atomic number Z, is (dP)/(dr) = (4Z^(3))/(a_(0)^(3))(2r-(2Zr^(2))/(a_(0)))e^(-2Ze//a_(0)) . Then which of the following statements is/are correct

If A,A_(1),A_(2),A_(3) are the areas of incircle and ex-circle of a triangle respectively then prove that (1)/(sqrt(A_(1)))+(1)/(sqrt(A_(2)))+(1)/(sqrt(A_(3)))=(1)/(sqrt(A))

If log_(e )((1+x)/(1-x))=a_(0)+a_(1)x+a_(2)x^(2)+…oo then a_(1), a_(3), a_(5) are in

If A, A_(1),A_(2),A_(3) are areas of excircles and incircle of a triangle, then (1)/(sqrt(A_(1)))+(1)/(sqrt(A_(2)))+(1)/(sqrt(A_(3)))=

Using mathematical induction, the numbers a_(n)'s are defined by, a_(0) =1, a_(n+1) = 3n^(2) + n+a_(n) ( n ge 0) . Then a_(n) =