Zeff, also known as effective nuclear charge or effective nuclear charge experienced by an electron, is a concept used in atomic structure to describe the net positive charge experienced by an electron in an atom. It takes into account the shielding effect of other electrons in the atom.
For beryllium (Be), the atomic number is 4, which means it has four protons in its nucleus. In a neutral beryllium atom, the number of electrons is also 4, matching the number of protons.
To determine Zeff for beryllium, we consider the electron-electron repulsion and shielding effects. The two inner electrons (with principal quantum numbers of 1 and 2) shield the outermost electrons from the full nuclear charge. Therefore, the two outermost electrons experience a reduced effective nuclear charge.
The effective nuclear charge experienced by the outermost electrons in beryllium can be estimated as follows:
Zeff = Z - S
where Z is the atomic number (number of protons) and S is the screening constant or the number of inner electrons.
In the case of beryllium, the screening constant (S) is 2, considering the two inner electrons (1s^2 configuration) that shield the outermost electrons from the full nuclear charge.
Therefore, the effective nuclear charge (Zeff) for beryllium is:
Zeff = 4 - 2 = 2
Hence, the outermost electrons in beryllium experience an effective nuclear charge of +2.