# 2.18 In a hydrogen atom, the electron and proton are bound at a distance of about $0.53 \dot{A}$(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)?

the potential energy of the system is -27.2eV. (from the previous question)

Kinetic energy is half of the potential energy in magnitude. so

Kinetic energy = 27/2 = 13.6eV

so,

Total energy = 13.6 - 27.2 = -13.6eV

Hence the minimum work required to free the electron is 13.6eV

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