Satellites and Binding Energy EX 7

The electrons are supplied with energy $E_{supplied}$ of 8.3 eV. The electrons escaping from the sheet of lithium are observed to move with kinetic energy of 6 eV.

The electrons are bound in the metal and therefore have some energy $E<0$. The binding energy is the absolute value value of their energy, or, $\left\vert E\right\vert$. The energy supplied to each electron is a sum of the binding energy and the kinetic energy. In symbolic terms, $E_{supplied}=\left\vert E\right\vert +K$. Substituting into this equation we get $8.3=\left\vert E\right\vert +6$. Therefore $\left\vert E\right\vert$ = 2.3 eV. This is the binding energy of the electrons in lithium. Consequently, the energy of the electrons in lithium is -2.3 eV.