The first ionization energy of sodium is 496 kJ/mol. Use Coulomb's law to estimate the average distance between the sodium nucleus and the 3s electron. How does this distance compare to the atomic radius of sodium? Explain the difference.

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Identify the given information: The first ionization energy of sodium is 496 kJ/mol.

Recall Coulomb's law: \( F = \frac{k \cdot |q_1 \cdot q_2|}{r^2} \), where \( F \) is the force between two charges, \( k \) is Coulomb's constant, \( q_1 \) and \( q_2 \) are the charges, and \( r \) is the distance between the charges.

Convert the ionization energy from kJ/mol to J/atom by dividing by Avogadro's number.

Use the relationship between energy and force: \( E = F \cdot r \), where \( E \) is the ionization energy, to solve for \( r \). Rearrange to find \( r = \frac{k \cdot |q_1 \cdot q_2|}{E} \).

Compare the calculated distance \( r \) to the known atomic radius of sodium, and discuss why the ionization energy distance might differ from the atomic radius, considering factors like electron shielding and effective nuclear charge.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Ionization Energy

Ionization energy is the energy required to remove an electron from an atom in its gaseous state. For sodium, the first ionization energy of 496 kJ/mol indicates the energy needed to remove the outermost 3s electron. This concept is crucial for understanding the strength of the attraction between the nucleus and the electrons, which directly influences the distance between them.

Coulomb's Law

Coulomb's law describes the electrostatic interaction between charged particles, stating 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. In this context, it helps estimate the average distance between the sodium nucleus and its 3s electron by relating the ionization energy to the attractive force acting on the electron.

Atomic Radius

The atomic radius is a measure of the size of an atom, typically defined as the distance from the nucleus to the outermost electron shell. For sodium, the atomic radius provides a context for comparing the calculated distance from the nucleus to the 3s electron. Differences between this distance and the atomic radius can arise due to electron shielding and the distribution of electron density in the atom.