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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 dPdr=4Z3a30(2r2Zr2a0)e2Zra0. Which of the following statements is/are correct?


Correct Answer
A
At the maximum value of the radial distribution function dP(r)dr=0, one antinode is present
Correct Answer
B
Most probable radius of Li2+ is a02 pm
Correct Answer
C
Most probable radius of He+ is a02 pm
Correct Answer
D
Most probable radius of hydrogen atom is a0 pm

Solution

The correct options are
A At the maximum value of the radial distribution function dP(r)dr=0, one antinode is present
B Most probable radius of Li2+ is a02 pm
C Most probable radius of He+ is a02 pm
D Most probable radius of hydrogen atom is a0 pm
At the point of maximum value of radial distribution function(RDF),
dPdr=0
(2r2Zr2a0=0);r=a0Z
where Z=3 for Li2+ and Z=2 for He+; Z=1 for hydrogen.

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