Q. 193.8( 5 Votes )

# If one of the two electrons of a H_{2} 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 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.

Answer :

The system of two protons and electron is represented as below,

The total potential energy at infinity is Zero.

Thus, Potential energy of the system is,

V =

Where,

Charge on proton 1, q_{1} = 1.6 × 10^{-19} C

Charge on proton 2, q_{2} = 1.6 × 10^{-19} C

Charge on electron, q_{3} = - 1.6 × 10^{-19} C

Distance between proton 1 and proton 2, d_{1} = 1.5 × 10^{-10} m

Distance between proton 1 and electron, d_{2} = 1 × 10^{-10} m

Distance between proton 2 and electron, d_{3} = 1 × 10^{-10} m

ϵ_{0} = Permittivity of free space

and,

∴ V =

⇒ V = -30.7 × 10^{-19} J

Writing in electron volts, we get,

⇒ V = -19.2 eV

(∵ 1eV = 1.6 × 10^{-19} J)

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

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PREVIOUSIn a hydrogen atom, the electron and proton are bound at a distance of about 0.53 Å:(a) Estimate the potential energy of the system in eV, taking the zero of the potential energy at infinite separation of the electron from proton.(b) What is the minimum work required to free the electron, given that its kinetic energy in the orbit is half the magnitude of potential energy obtained in (a)?(c) What are the answers to (a) and (b) above if the zero of potential energy is taken at 1.06 Å separation?NEXTTwo charged conducting spheres of radii a and b are connected to each other by a wire. What is the ratio of electric fields at the surfaces of the two spheres? Use the result obtained to explain why charge density on the sharp and pointed ends of a conductor is higher than on its flatter portions.

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