Undergrad GRE related question in Quantum

[Silviu]

Hello! I was doing a GRE practice test and I came across this problem: The chlorine molecule consists of two chlorine atoms joined together by a covalent bond with length approximately 100 pm. What is the approximate kinetic energy of one if the covalently bonded electrons? And in their solution they use uncertainty principle: (100 pm)(delta p) = h => delta p = 2keV/c and then they plug this into E = p^2/2m. This is also what I would do during the exam, given the information provided by the problem. However, I am a bit confused about the correctness of the solution. The 100 pm is the actual length not the uncertainty in the length, so why can we use uncertainty principle like that? And even if that would be the case, how can you use the uncertainty in the momentum, to get the actual energy, using E = p^2/2m? Isn't something wrong here?

 

[BvU]

why can we use uncertainty principle like that

Because the expectation values of both $x$ and $p$ are zero from symmetry