The first ionization energy of lithium is 520 kJ/mol. Use Coulomb's law to estimate the average distance between the lithium nucleus and the 2s electron. How does this distance compare to the atomic radius of lithium? Assume an effective nuclear charge of 1+ for the valence electron.

Verified step by step guidance

1. Identify the given values: the first ionization energy (IE) of lithium is 520 kJ/mol, and the effective nuclear charge (Z_eff) is +1.
2. Convert the ionization energy from kJ/mol to joules per atom. Use the conversion factor: 1 kJ/mol = 1,000 J/mol and Avogadro's number (6.022 x 10^23 atoms/mol).
3. Apply Coulomb's law to relate the ionization energy to the distance (r) between the nucleus and the electron. Coulomb's law is given by: E = k * (Z_eff * e^2) / r, where E is the ionization energy, k is Coulomb's constant (8.99 x 10^9 N m^2/C^2), and e is the elementary charge (1.602 x 10^-19 C).
4. Rearrange the formula to solve for the distance r: r = k * (Z_eff * e^2) / E.
5. Compare the calculated distance r to the known atomic radius of lithium, which is approximately 152 pm (picometers).

Key Concepts

Ionization Energy

Ionization energy is the energy required to remove an electron from an atom in its gaseous state. For lithium, the first ionization energy is 520 kJ/mol, indicating the energy needed to remove the outermost electron. This concept is crucial for understanding the strength of the attraction between the nucleus and the electrons, which influences the distance between them.

Coulomb's Law

Coulomb's law describes the electrostatic interaction between charged particles. It states that the force between two charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. This law can be used to estimate the distance between the lithium nucleus and its valence electron by relating the ionization energy to the attractive force experienced by the electron.

Effective Nuclear Charge

Effective nuclear charge (Z_eff) is the net positive charge experienced by an electron in a multi-electron atom, accounting for shielding by other electrons. For lithium, an effective nuclear charge of 1+ means that the valence electron feels a reduced attraction due to the presence of the inner electron. This concept is essential for calculating the distance between the nucleus and the electron, as it influences the strength of the electrostatic force in Coulomb's law.