Question: In this problem you will estimate the radius and the energy of the lowest stationary state of the hydrogen atom using the uncertainty principle. The

In this problem you will estimate the radius and the energy of the lowest stationary state of the hydrogen atom using the uncertainty principle. The total energy of the electron of momentum p and mass m a distance r from the proton in the hydrogen atom is given by E = p²/2m – ke²/r, where k is the Coulomb constant. Assume that the minimum value of p² is p² ≈ (Δp)² = h²/r², where Δp is the uncertainty in p and we have taken Δr ~ r for the order of magnitude of the uncertainty in position; the energy is E = h²/2mr² – ke²/r. Find the radius r_m for which this energy is a minimum, and calculate the minimum value of E in electron volts.

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