In a hydrogen atom, the electron and proton are bound at a distanceof about 0.53 Å:
(a) Estimate the potential energy of the system in eV, takingthe zero of the potential energy at infinite separation of theelectron 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 ofpotential energy obtained in (a)?
(c) What are the answers to (a) and (b) above if the zero ofpotential energy is taken at 1.06 Å separation?
In a hydrogen atom, the electron and proton are bound at a distanceof about 0.53 Å:
(a) Estimate the potential energy of the system in eV, takingthe zero of the potential energy at infinite separation of theelectron 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 ofpotential energy obtained in (a)?
(c) What are the answers to (a) and (b) above if the zero ofpotential energy is taken at 1.06 Å separation?
The distance betweenelectron-proton of a hydrogen atom, 
Charge on an electron,q1 = −1.6 ×10−19 C
Charge on a proton, q2= +1.6 ×10−19 C
(a) Potential at infinity is zero.
Potentialenergy of the system, p-e = Potential energy atinfinity − Potential energy at distance, d
Where,
∈0is the permittivity of free space
Therefore,the potential energy of the system is −27.2 eV.
(b) Kinetic energy is half of the magnitude of potentialenergy.
Totalenergy = 13.6 − 27.2 = 13.6 eV
Therefore,the minimum work required to free the electron is 13.6 eV.
(c) When zero of potential energy is taken, 
∴Potentialenergy of the system = Potential energy at d1 −Potential energy at d
The distance betweenelectron-proton of a hydrogen atom,
Charge on an electron,q1 = −1.6 ×10−19 C
Charge on a proton, q2= +1.6 ×10−19 C
(a) Potential at infinity is zero.
Potentialenergy of the system, p-e = Potential energy atinfinity − Potential energy at distance, d
Where,
∈0is the permittivity of free space
Therefore,the potential energy of the system is −27.2 eV.
(b) Kinetic energy is half of the magnitude of potentialenergy.
Totalenergy = 13.6 − 27.2 = 13.6 eV
Therefore,the minimum work required to free the electron is 13.6 eV.
(c) When zero of potential energy is taken,
∴Potentialenergy of the system = Potential energy at d1 −Potential energy at d
