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If One of the Two Electrons of a H2 Molecule is Removed, We Get a Hydrogen Molecular Ion H_2^+. in the Ground State of an H_2^+` , the Two Protons Are Separated by Roughly 1.5 A and the Electron is Roughly 1 A from Each Proton. - Physics

If one of the two electrons of a Hmolecule is removed, we get a hydrogen molecular ion `H_2^+`. In the ground state of an `H_2^+` , the two protons are separated by roughly 1.5 Å, and the electron is roughly 1 Å from each proton. Determine the potential energy of the system. Specify your choice of the zero of potential energy.

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Solution

The system of two protons and one electron is represented in the given figure.

Charge on proton 1, q1 = 1.6 ×10−19 C

Charge on proton 2, q2 = 1.6 ×10−19 C

Charge on electron, q3 = −1.6 ×10−19 C

Distance between protons 1 and 2, d1 = 1.5 ×10−10 m

Distance between proton 1 and electron, d2 = 1 ×10−10 m

Distance between proton 2 and electron, d3 = 1 × 10−10 m

The potential energy at infinity is zero.

Potential energy of the system,

`V=(q_1q_2)/(4piin_0d_1)+(q_2q_3)/(4piin_0d_3)+(q_3q_1)/(4piin_0d_2)`

Substituting `1/(4piin_0)=9xx10^9 Nm^2 C^-2`, we obtain

`V=(9xx10^9xx10^-19xx10^-19)/(10^-10)[-(16)^2+(1.6)^2/(1.5)-(1.6)^2]`

`=-30.7xx10^-19 J`

`=-19.2 eV`

Therefore, the potential energy of the system is −19.2 eV.

Concept: Potential Energy of a System of Charges
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APPEARS IN

NCERT Class 12 Physics Textbook
Chapter 2 Electrostatic Potential and Capacitance
Q 19 | Page 90
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