Use Coulomb's law to calculate the ionization energy in kJ / mol of an atom composed of a proton

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Use Coulomb's law to calculate the ionization energy in kJ /...

Use Coulomb's law to calculate the ionization energy in $\mathrm{kJ} / \mathrm{mol}$ of an atom composed of a proton and an electron separated by $100.00 \mathrm{pm} .$ What wavelength of light has sufficient energy to ionize the atom?

Key Concepts

Relation Between Photon Energy and Wavelength

The relationship between a photon's energy and its wavelength is given by the equation E = hc/?, where h is Planck's constant and c is the speed of light. This concept is crucial for determining what wavelength of light carries enough energy to ionize an atom. By rearranging the equation, one can compute the required wavelength based on the ionization energy, thereby connecting concepts from both quantum mechanics and electromagnetic theory.

Photon Energy and the Planck Relation

The energy of a photon is determined by the Planck relation, which states that the energy is directly proportional to its frequency, with Planck's constant as the proportionality factor (E = h?). This concept bridges the particle and wave nature of light, indicating that light can deliver quantized amounts of energy. It is fundamental in linking electromagnetic radiation to quantum phenomena, including the process of ionization when a photon with sufficient energy interacts with an atom.

Ionization Energy

Ionization energy refers to the minimum amount of energy required to remove an electron from an atom or ion in its ground state. This concept is central to understanding atomic stability and reactivity, and it is measured in energy per mole, typically in kJ/mol. The calculation of ionization energy using principles like Coulomb's law provides insights into the electronic structure and the energy required to overcome the electrostatic forces binding the electron to the nucleus.

Coulomb's Law

Coulomb's Law is a fundamental principle in electromagnetism that quantifies the force between two point charges. In the context of atomic physics, it is used to calculate the electrostatic potential energy between charges, such as that between a proton and an electron. The law states that the force is directly proportional to the product of the charges and inversely proportional to the square of the distance separating them, which helps in understanding and quantifying the energy interactions within atoms.

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