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(D) For a $1s$ orbital of a hydrogen atom, the radial wave function is given by $R(r) = 2(Z/a_0)^{3/2} e^{-Zr/a_0}$.The radial probability distributio

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(D) For a $1s$ orbital of a hydrogen atom, the radial wave function is given by $R(r) = 2(Z/a_0)^{3/2} e^{-Zr/a_0}$.The radial probability distribution function $P(r)$ is defined as the probability of finding the electron in a spherical shell of thickness $dr$ at a distance $r$ from the nucleus.$P(r) = 4\pi r^2 R^2(r) dr$.Substituting the expression for $R(r)$, we get $P(r) = 4\pi r^2 [2(Z/a_0)^{3/2} e^{-Zr/a_0}]^2 dr = 16\pi (Z/a_0)^3 r^2 e^{-2Zr/a_0} dr$.At $r = 0$, $P(r) = 0$ because of the $r^2$ term.As $r 	o \infty$, $P(r) 	o 0$ because of the exponential decay term $e^{-2Zr/a_0}$.The function $P(r)$ starts from zero, increases to a maximum value at $r = a_0/Z$, and then decreases asymptotically to zero.This corresponds to the shape shown in Graph $D$.

$P$ is the probability of finding the $1s$ electron of a hydrogen atom in a spherical shell of infinitesimal thickness, $dr$, at a distance $r$ from the nucleus. The volume of this shell is $4\pi r^2 dr$. The qualitative sketch of the dependence of $P$ on $r$ is:

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