The figure below is the plot of potential energy versus internuclear distance $(𝑑)$ of $H_{2}$ molecule in the electronic ground state. What is the value of the net potential energy $E_{0}$ (as indicated in the figure) in $k J m o l^{- 1}$ , for $d = d_{0}$ at which the electron-electron repulsion and the nucleus-nucleus repulsion energies are absent? As a reference, the potential energy of an atom is taken as zero when its electron and the nucleus are infinitely far apart. Use Avogadro constant as 6.023 × 10²³ mol⁻¹.

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Solution

Step 1: Given data:
Avogadro constant as $6.023 \times 10^{23} m o l^{- 1}$
For $d = d_{0}$ at which the electron-electron repulsion and the nucleus-nucleus repulsion energies are absent.

The plot of potential energy versus internuclear distance $(𝑑)$ of $H_{2}$ molecule
Step 2: Formula used:
P. E of 2 H-atoms
Total energy $= \frac{P E}{2}$
Potential Energy $= 2 T o t a l E n e r g y \dots \dots \dots \dots (1)$
Therefore, from the above equation, it is clear that potential energy is two times the total energy
Step 3: Calculation of the value of the net potential energy $E_{0}$
Potential energy between two hydrogen atom is given by
$E = \frac{{kq}_{1} q_{2}}{r} where k is constant, r is seperation betweeen them, q is charge$
r can be calculate by sing
$r = 0.529 \times \frac{n^{2}}{z} f o r g r o u n d s t a t e n = 1 f o r H - a t o m z = 1 r = 0.529 A$
Where, $z$ is the atomic number
$n = 1$ is ground state
$E = \frac{{kq}_{1} q_{2}}{r} a s q_{1}, q_{2} a r e s a m e (b o t h a r e e l e c t r o n) E = \frac{k q^{2}}{r} E = \frac{9 \times 10^{9} \times {(1.6 \times 10^{- 19})}^{2}}{0.59 \times 10^{- 10}}$
Total Energy = 2time potential energy of 1 H atom
$T o t a l E n e r g y = 2 E$
Potential energy per mole
$E = \frac{9 \times 10^{9} \times {(1.6 \times 10^{- 19})}^{2}}{0.59 \times 10^{- 10}} \times 6.023 \times 10^{23}$
Solving this we will get $5242.42 K J / m o l$
Hence, $5242.42 K J / m o l$ is the value of the net potential energy $E_{0}$ (as indicated in the figure) in $k J m o l^{- 1}$

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Similar questions

Q. The figure below is the plot of potential energy versus internuclear distance (𝑑) of

H_{2}

molecule in the electronic ground state. What is the value (only magnitude) of the net potential energy

E_{0}

(as indicated in the figure) in

k J m o l^{- 1}

, for

d = d_{0}

at which the electron-electron repulsion and the nucleus-nucleus repulsion energies are absent? As reference, the potential energy of

H

atom is taken as zero when its electron and the nucleus are infinitely far apart. Use Avogadro constant as

6.023 \times 10^{23} mol^{- 1}

Q. As we move away from the nucleus, in atom the potential energy of electron increases, the total energy as a whole increases. But what happens to the kinetic energy of the electron?

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Energy of an electron increases with increase in distance from the nucleus. Comment on the change in kinetic energy and potential energy.

Though the kinetic energy of electrons decreases with an increase in the distance from the nucleus, the potential energy of the electron increases. How do you account for this?

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