The radial distribution functions -Pr- is used to determine the most probable radius- which is used to find the electron in a given orbital dPrdr for 1s-orbital of hydrogen like atom having atomic number Z- is dPdr-4Z3-a03 2r-2Zr2a0 e-2Zra0- Which of the following statements is-are correct-

At the point of maximum value of radial distribution function(RDF), dPdr=0 ( 2r 2Zr^2a_0=0 ); r=a_0Z where Z=3 for Li^2+ and Z=2 for He^+; Z=1 for hydrogen. ...

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Standard XII

Chemistry

Shapes of Orbitals and Nodes

The radial di...

Question

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 1s-orbital of hydrogen like atom having atomic number $Z$ , is $\frac{d P}{d r} = \frac{4 Z^{3}}{a_{0}^{3}} (2 r - \frac{2 Z r^{2}}{a_{0}}) e^{\frac{- 2 Z r}{a_{0}}}$ . Which of the following statements is/are correct?

At the maximum value of the radial distribution function

\frac{d P (r)}{d r} = 0

, one antinode is present

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Most probable radius of

L i^{2 +}

\frac{a_{0}}{2} pm

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Most probable radius of

H e^{+}

\frac{a_{0}}{2} pm

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Most probable radius of hydrogen atom is

a_{0} pm

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Solution

The correct option is D Most probable radius of hydrogen atom is $a_{0} pm$
At the point of maximum value of radial distribution function(RDF),
$\frac{d P}{d r} = 0$
$(2 r - \frac{2 Z r^{2}}{a_{0}} = 0); r = \frac{a_{0}}{Z}$
where $Z = 3$ for $L i^{2 +}$ and $Z = 2$ for $H e^{+}$ ; $Z = 1$ for hydrogen.

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Similar questions

Q. 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 1s-orbital of hydrogen like atom having atomic number

Z

, is

\frac{d P}{d r} = \frac{4 Z^{3}}{a_{0}^{3}} (2 r - \frac{2 Z r^{2}}{a_{0}}) e^{\frac{- 2 Z r}{a_{0}}}

. Which of the following statements is/are correct?

Q. 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 1s - orbital of hydrogen-like atom having atomic number Z, is

\frac{d P}{d r} = \frac{4 Z^{3}}{a_{0}^{3}} (2 r - \frac{2 Z r^{2}}{a_{0}}) e^{- 2 Z r / a_{0}}

Then which of the following statements is/are correct?

Q. If 4 times the most probable distance of electron of a 1s orbital in a unielectronic atom /ion is given by

0.529 A^{\circ}

then the atomic number of the unielectronic species will be. [Given: Wave function of 1s orbital,

Ψ = \sqrt{(\frac{Z^{3}}{π a_{0}^{3}})} e^{- Z r / a_{0}}

where

a_{0}

= radius of first Bohr's orbital in H - atom = (52.9 pm) and Z is atomic number of unielectronic species]

Q. 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. The wave function for

1 s

orbital of the hydrogen atom is given by

Ψ_{1 s} = \frac{π}{\sqrt{2}} e^{- r / a_{0}}

where

a_{0} =

Radius of first Bohr orbit

r =

Distance from the nucleus (Probability of finding the electron varies with respect to it)

What will be the ratio of probabilities of finding the electrons at the nucleus to first Bohr's orbit

a_{0}

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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 dP(r)dr for 1s-orbital of hydrogen like atom having atomic number Z, is dPdr=4Z3a30(2r−2Zr2a0)e−2Zra0. Which of the following statements is/are correct?

The correct option is D Most probable radius of hydrogen atom is a0 pmAt the point of maximum value of radial distribution function(RDF), dPdr=0 (2r−2Zr2a0=0);r=a0Z where Z=3 for Li2+ and Z=2 for He+; Z=1 for hydrogen.