The radial distribution function `[P(r)]` is used to determine the most probble radius, which is used to find the electron in a givenorbital. `(dp(r))/(dr)` for `1s`- orbital of hydrogen like atom having atomic number Z, is `(dp)/(dr)=(4Z^(3))/(a_(o)"^(3))(2r-(2Zr^(2))/(a_(o)))e^(-2zr//a_(o)):`
Then which of the following statements is/are correct ?

Options

A. At the point maximum value of radial distribution function `(dP(r))/(dr)=0`, one antinode is present
B. Most probable radius of `Li^(2+)` is `a_(0)/3` pm
C. Most probable radius of `He^(+)` is `a_(0)/2` pm
D. Most probable radius of hydrogen atom is `a_(0)` pm

Answer

A, B, C, D

Explanation

At the point of maximum value of RDF
`(dP)/(dr)=0`
`(2r-(2Zr^(2))/a_(0))=0, r=a_(0)/Z`
where `Z=3` for `Li^(2+)` and `Z=2` for the `He^(+), Z=1` for hydrogen.