what represents the radial probability density of finding an electron

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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. 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. Which of the following is true ?
a) φ2(r) represent probability density of electron
b) RPF(Radial Probability Function) represent probability of electron in spherical region of unit thickness
c) There is not any radial node in 1s orbital
1) only (a)
2) Both a, b
3) Both b, c
4) a, b ,c

Graph of Radial Probability density v/s distance r of the electron from nucleus of 2s can be

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