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

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Coulomb's Law The attractions and repulsions between charged particles, first introduced in Section 2.4, are described by Coulomb's law, which states that the potential energy (E) of two charged particles depends on their charges (9₁ and 92) and on their separation (r): 19192 E [9.1] In this equation, Eo is a constant (o= 8.85 x 10-12 C²/J.m). The potential energy is positive for charges of the same sign (plus x plus, or minus x minus) and negative for charges of opposite sign (plus x minus, or minus x plus). The magnitude of the poten- tial energy depends inversely on the separation between the charged particles. We can draw three important conclusions from Coulomb's law: Απερ r ■ For like charges, the potential energy (E) is positive and decreases as the particles get farther apart (as r increases). Since systems tend toward lower potential energy, like charges repel each other (in much the same way that like poles of two magnets repel each other). ■ For opposite charges, the potential energy is negative and becomes more negative as the particles get closer together (as r decreases). Therefore, opposite charges (like opposite poles on a magnet) attract each other. ■ The magnitude of the interaction between charged particles increases as the charges of the particles increase. Consequently, an electron with a charge of 1-is more strongly attracted to a nucleus with a charge of 2+ than it is to a nucleus with a charge of 1+.