59.difference between radial difference probability function and radial provability density and radial wave function

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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

Q. The radial probability distribution curve obtained for an orbital wave function

(Ψ)

has

3

peaks and

2

radial nodes. The valence electron of which one of the following metals does this wave function

(Ψ)

correspond to?

Q. The number of radial nodes present in the radial probability distribution curves for the orbital wave function with quantum numbers it n= 4, l= 0 and m=0 is :

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)

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 $(x + y)$ .

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