Question

A triply ionized beryllium atom has an electron in the n = 3 state. What is the electric potential energy of the electron? Answer is not 48.356 eV

Answer 1

We know that the Total Energy E of an electron in the nth shell of a Hydrogen-like model is given by

where Z is the atomic number of the atom,   is the Coulomb's constant = 9*(10^9) N(m^2)/(C^2), e is the electronic charge = 1.6*(10^-19) C, is the mass of an electron = 9.1*(10^-31) kg, h is the Planck's constant = 6.64*10^-34 Js, and n is the shell number

This can be approximated to

Since the atomic number of Beryllium is 4 and n = 3,

E= -13.6*16/9 = -24.178 eV

And since the Potential Energy of the Electron is 2E,

The Potential Energy of the electron is -48.356 eV