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## Homework Statement

Question 26 of the physics GRE from the practice test available here: https://www.ets.org/gre/subject/about/content/physics/

The normalized ground state wave function of hydrogen is [itex]\psi_{100}=\frac{2}{(4\pi)^{1/2}a_0^{3/2}}e^{-r/a_0}[/itex], where [itex]a_0[/itex] is the Bohr radius. What is the most likely distance that the electron is from the nucleus?

(A) 0

(B) [itex]a_0/2[/itex]

(C) [itex]a_0/\sqrt{2}[/itex]

(D) [itex]a_0[/itex]

(E) [itex]2a_0[/itex]

## Homework Equations

Given in question.

## The Attempt at a Solution

This seems like a really poorly worded question to me (at least, based on what answer they're looking for). The answer, according to the booklet, is (D). This (obviously) is the expectation value for the radial distance. However, the

*most likely*distance that the electron is from the nucleus is just the distance corresponding to maximum value for the wavefunction's squared norm. This would be (A). So, is my reading of the question right? And if it's right, is this horrible abuse of language standard? If it's not standard, then the question is just plain wrong, and it certainly doesn't inspire much confidence in the physics GRE if that's the case.