(Solution) - Consider a simple model of the helium atom in which -(2025 Original AI-Free Solution)

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Consider a simple model of the helium atom in which two electrons, each with mass m, move around the nucleus (charge +2e) in the same circular orbit. Each electron has orbital angular momentum Ii (that is, the orbit is the smallest-radius Bohr orbit), and the two electrons are always on opposite sides of the nucleus. Ignore the effects of spin.
(a) Determine the radius of the orbit and the orbital speed of each electron.
(b) What is the total kinetic energy of the electrons?
(c) What is the potential energy of the system (the nucleus and the two electrons)?
(d) In this model, how much energy is required to remove both electrons to infinity? How does this compare to the experimental value of 79.0eV?