Use Coulomb's law to calculate the ionization energy in kJ/mol of an atom composed of a proton and an electron separated by 176.00 pm .
To calculate the ionization energy of an atom using Coulomb's law, we need to consider the interaction between the proton and electron. The ionization energy is the amount of energy required to remove an electron from the atom, resulting in a positively charged particle (ion).
Coulomb's law describes the strength of the electrostatic force between two charged particles. It is given by the equation:
F = (k * q1 * q2) / r^2
where:
F is the electrostatic force between the particles,
k is Coulomb's constant (8.99 × 10^9 N m^2/C^2),
q1 and q2 are the charges of the particles (in coulombs),
and r is the distance between the particles (in meters).
However, in this case, we need to calculate the ionization energy, which is the energy required to remove an electron from the atom. The ionization energy (IE) can also be expressed in terms of Coulomb's law:
IE = (k * q1 * q2) / r
where IE is the ionization energy.
In this scenario, we have a proton (q1) with a positive charge and an electron (q2) with a negative charge. The charges of a proton and electron are equal in magnitude but opposite in sign. Therefore, we can simplify the equation:
IE = (k * q^2) / r
where q is the magnitude of the charge of a proton or electron (the elementary charge, 1.602 × 10^-19 C) and r is the distance between them.
Now, we can substitute the given values into the equation:
IE = (k * q^2) / r
= [(8.99 × 10^9 N m^2/C^2) * (1.602 × 10^-19 C)^2] / (176.00 × 10^-12 m)
≈ 1158.26 kJ/mol
Therefore, the ionization energy of the atom is approximately 1158.26 kJ/mol.