## GR0877 Problem 26

**PROBLEM STATEMENT**: *This problem is still being typed*.

**SOLUTION**: (**D**) The probability that the electron will be found between and is . The most probable value is given by the maximum of the probability density (take the second derivative if you want to convince yourself that it is indeed the maximum): . Plugging in: . From this, one has , which is nothing else but the Bohr radius.

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For those (like me) who don’t wanna do that calculation on the test, the most probably radius for the ground state of H is a_o, the Bohr radius. Makes perfect sense. The expectation value is 1.5a_o, though, due to the tiny contributions from the finite probabilities of finding the electron at a larger radius. Don’t ask me how to calculate that; I just memorized it!

Where does the 4*pi*r^2*dr come from as dV?

It’s a volume of a spherical shell between and .