Physics Class 12 NCERT Solutions: Chapter 2 Electrostatic Potential and Capacitance Part 8

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Relation between potential difference and work done

Relation between Potential Difference and Work Done

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Q: 18. In a hydrogen atom, the electron and proton are bound at a distance of about .

(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 separation?

Answer:

The distance between electron-proton of a hydrogen atom,

Charge on an electron,

Charge on a proton,

(A) Potential at infinity is zero.

Potential energy of the system, PE = Potential energy at infinity Potential energy at distance, d

Where,

is the permittivity of free space

Potential energy

Since, ,

Potential energy

Therefore, the potential energy of the system is .

(B) Kinetic energy is half of the magnitude of potential energy.

Kinetic energy

Total energy

Therefore, the minimum work required to free the electron is .

(C) When zero of potential energy is taken,

Potential energy of the system Potential energy at Potential energy at d

Q: 19. If one of the two electrons of a molecule is removed, we get a hydrogen molecular ion . In the ground state of an, , the two protons are separated by roughly , and the electron is roughly 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 one electron is represented in the given figure.

Q 19 The System of Two Protons and One Electron

Q 19 the System of Two Protons and One Electron

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Charge on proton,

Charge on proton,

Charge on electron,

Distance between protons 1 and 2,

Distance between proton 1 and electron,

Distance between proton 2 and electron,

The potential energy at infinity is zero.

Potential energy of the system,

Substituting

Therefore, the potential energy of the system is.