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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. \( \frac{d P(r)}{d r} \) for \( 1 s \)-orbital of hydrogen like atom having atomic number \( Z \), is \( \frac{d P}{d r}=\frac{4 Z^{3}}{a_{0}^{3}}\left(2 r-\frac{2 Z r^{2}}{a_{0}}\right) e^{-2 Z r / a_{0}} \) :
Then which of the following statements is/are correct?
(a) At the point of maximum value of radial distribution function \( \frac{d P(r)}{d r}=0 \); one antinode is present
(b) Most probable radius of \( \mathrm{Li}^{2+} \) is \( \frac{a_{0}}{3} \mathrm{pm} \)
(c) Most probable radius of \( \mathrm{He}^{+} \)is \( \frac{a_{0}}{2} \mathrm{pm} \)
(d) Most probable radius of hydrogen atom is \( a_{0} \mathrm{pm} \)
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