What is radial wave function probability density

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Q. For

1 s

orbital of Hydrogen atom radial wave function is given as:

R (r) = \frac{1}{\sqrt{π}} {(\frac{1}{a_{0}})}^{3 / 2} e^{- r / a_{0}}

where

a_{0} = 0.529 A \circ)

The ratio of radial probability density of finding electron at

r = a_{o}

to the radial probability density of finding electron at the nucleus is given as (x.e

^{- y}

). Calculate the value of (x + y)

Q. Assertion: The plots of the probability density and the radial probability function versus distance

r

from the nucleus for any particular orbital are not identical.

Reason: Probability density is

ψ^{2}

whereas radial probability function represents the probability of finding electrons in a shell of thickness

d r

For the $1 s$ orbital of the Hydrogen atom, the radial wave function is given as:
$R (r) = \frac{1}{\sqrt{π}} {(\frac{1}{a_{0}})}^{\frac{3}{2}} e^{\frac{- r}{a_{0}}}$ (Where $a_{0} = 0.529 \circ A$ )

The ratio of radial probability density of finding an electron at $r = a_{0}$ to the radial probability density of finding an electron at the nucleus is given as $(x . e^{- y})$ .
Calculate the value of $(x + y)$ .

Q. Which among the following statements is/are correct?

ψ^{2}

represents the atomic orbitals

b) The number of peaks in radial probability distribution is

(n - 1)

c) Radial probability density

P_{n i} (r) = 4 π r^{2} R_{n i}^{2} (r)

d) A node is a point in space where the wave function

(Ψ)

has zero amplitude

Q. The number of nodes observed in radial probability distribution curves if the wave function is

Ψ 310

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