Question

The radial distribution functions `[P(r)]` is used 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^(-2Zr//a_(0))` :
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 1

Correct Answer - A, B, C, D
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.