To determine the number of valence electrons in a germanium (Ge) atom in the ground state, follow these steps:
1. Identify the atomic number of germanium: Germanium has an atomic number of 32, which means it has 32 electrons in a neutral atom.
2. Write the electron configuration of germanium:
The electrons are filled into various orbitals in the order of increasing energy levels. The electron configuration for germanium is:
[tex]\( 1s^2 \, 2s^2 \, 2p^6 \, 3s^2 \, 3p^6 \, 4s^2 \, 3d^{10} \, 4p^2 \)[/tex]
3. Determine the valence electrons:
Valence electrons are the electrons located in the outermost shell of an atom. For germanium, the outermost shell is the fourth shell (n = 4).
From the electron configuration, the fourth shell contains:
- [tex]\( 4s^2 \)[/tex] (2 electrons)
- [tex]\( 4p^2 \)[/tex] (2 electrons)
4. Calculate the total number of valence electrons:
Add the electrons in the [tex]\( 4s \)[/tex] and [tex]\( 4p \)[/tex] orbitals:
[tex]\[
\text{Valence electrons} = 4s^2 + 4p^2 = 2 + 2 = 4
\][/tex]
Therefore, the total number of valence electrons in an atom of germanium in the ground state is [tex]\( \boxed{4} \)[/tex].
