Here's how to determine the energy of an electron in the ground state of a hydrogen-like atom with Z = 4:

Understanding Rydberg's Formula

Rydberg's formula gives the energy levels of an electron in a hydrogen-like atom:

E = -13.6 * (Z^2 / n^2) eV

Where:

* E is the energy of the electron (in electron volts, eV)

* Z is the atomic number (number of protons)

* n is the principal quantum number (1 for the ground state)

Applying the Formula

1. Z = 4: This means we're dealing with an atom with 4 protons (like beryllium).

2. n = 1: We're interested in the ground state, so the principal quantum number is 1.

Plugging these values into the formula:

E = -13.6 * (4^2 / 1^2) eV

E = -13.6 * 16 eV

E = -217.6 eV

The Answer

The energy of the electron in the ground state of a hydrogen-like atom with Z = 4 is -217.6 eV.

Important Note: This is the energy relative to the ionized state (when the electron is completely removed from the atom). The energy is negative because the electron is bound to the nucleus.