3. [10 pts] Calculate the radius of the sphere that encloses 92% of the ground state of the hydrogen atom. Express your answer in Ångstroms and you must explicitly integrate over r, ϕ and θ.
HINT: This problem cannot be solved analytically, and there will be a point where the solution must be found numerically. Tabulate your trial and error numerical solution. You can use a spreadsheet program like Excel to solve for the radii within one decimal place by trial and error.
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