Final answer:
To estimate the effective nuclear charge on the 2s electron in a Li atom, one must use the ionization energy of Li (5.39 eV) and apply the formula for the energy levels of hydrogen-like atoms. By rearranging this formula and converting the ionization energy into joules, we can solve for the effective nuclear charge, which is about +1.26 proton charges for Li.
Step-by-step explanation:
To estimate the effective nuclear charge (Zeff) experienced by the 2s electron in a lithium (Li) atom, we reference the ionization energy of Li, which is 5.39 eV for the removal of its outermost electron. In the context of the Bohr model for hydrogen-like atoms, the ionization energy is related to the effective nuclear charge.
Let's consider a hydrogen-like ion with an atomic number Z and a single electron. The energy levels for such a system can be expressed using the formula E = -kZ2/n2, where k is a constant with the value 2.179 × 10-18 J, Z is the effective nuclear charge, and n is the principal quantum number of the electron's orbital.
The first ionization energy of Li corresponds to the energy difference when an electron is removed from the n = 2 state. Since we know the ionization energy (5.39 eV) and the constant k, we can rearrange the energy level formula to solve for Zeff as follows:
5.39 eV = - E
= -(-kZeff2/4)
=> Zeff = sqrt((5.39 eV × 1.602 × 10-19 C/eV) × 4 / (2.179 × 10-18 J))
=> Zeff (in units of proton charge)
The conversion factor between eV and J (1 eV = 1.602 × 10-19 C) is used to make units consistent. Calculating Zeff, we find it to be approximately 1.26 for Li, indicating that the 2s electron in a Li atom experiences an effective nuclear charge of about +1.26 proton charges.
The effective nuclear charge is an important concept in understanding atomic structure, and it helps explain trends across the periodic table, such as the steady decrease in atomic size from Li to Ne in the second row. This concept is also helpful in predicting the chemical properties and reactivity of elements, as it influences the attraction between the nucleus and valence electrons.