# why is total electron energy of an electron in metal negative?

In my textbook, it says that any electron bound in metals, modelled as some potential well $U$, has negative total electron energy, as shown below in the figure.

Why is the total electron energy negative? And how can this be possible?

Secondly, the (b) part (it is below the (a) part) of the figure is the graph of the potential energy seen by electrons. I am curious why the part $x<0$ has $-U$ as its potential energy seen by electrons. The textbook stated that the metal works(or is modelled) as the potential well depth $U$. So why is it suddenly $-U$?

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Because zero is the energy of an electron far away, and it takes energy to pull the electron out. –  Ron Maimon Aug 7 '12 at 22:14

What about the second part? Why is the potential energy seen by electrons negative in $x<0$? (The text confuses me: it says that the potential well is the depth $U$, yet it says that potential seen by electrons is $-U$... –  Mark Lucas Aug 7 '12 at 22:33
@MarkLucas: you're modeling the binding of the electrons--when they are bound by the metal, they have a potential U below their free state. Just like if you were stuck in a pit with depth $h$, you would be $-h$ meters above the ground. –  Jerry Schirmer Aug 7 '12 at 22:46