It has been measured that it required 0.850 eV to remove an electron from the hydrogen atom. In what state was the atom before the ionization happened?

Understanding energy conversion is crucial when dealing with exercises in atomic physics, especially when we want to relate the energy associated with electrons in atoms to more familiar units of measurement. In the given exercise, energy conversion is used to switch from the electron volt (eV) to joules (J), the SI unit for energy. An electron volt is the amount of kinetic energy gained or lost by a single electron when it moves across an electric potential difference of one volt.

To convert the measurement of 0.850 eV to joules, we use the conversion factor of 1 eV equaling approximately 1.602 x 10^-19 Joules. Therefore, the energy in joules is calculated by multiplying 0.850 eV by this conversion factor, resulting in an energy value in joules that can then be used for further calculations or comparisons.

The electron volt (eV) is a unit of energy that is particularly useful in atomic physics and quantum mechanics. It provides a scale for energy that is appropriate for the interactions and transitions that occur at the atomic and subatomic levels.

While not an SI unit, the eV is widely used because it translates large and abstract quantities of energy into manageable numbers. For example, one eV is equivalent to the energy one electron gains when accelerating through an electric potential difference of one volt. This unit is also particularly relevant in the context of ionizing an atom, which means removing an electron from the atom, as it gives a direct measure of energy often encountered in these processes.

Atomic physics studies the behavior of electrons, protons, and neutrons, which make up atoms. It particularly focuses on the electron configurations around the nucleus and the energy levels those electrons occupy.

In the context of our exercise, understanding the hydrogen atom—one of the simplest and most fundamental systems in atomic physics—is key. The hydrogen atom consists of a single electron orbiting a single proton. Ionization energy is a significant concept here, referring to the amount of energy required to completely remove an electron from its atomic orbit. With only one electron, the ionization energies for a hydrogen atom can be calculated, and differ for each quantum state the electron may occupy.

Quantum states are the distinct states of an atom or particle characterized by specific quantized energy levels in the realm of quantum physics. In the hydrogen atom, these states are based on the principal quantum number, represented by 'n', which can take any positive integer value. Each value of 'n' corresponds to a different energy level and is associated with a specific orbit or shell.

The energy for a given state 'n' in a hydrogen atom is given by the formula \( E_n = - \frac{13.6 \text{ eV}}{n^2} \). When we know the ionization energy required to remove an electron, we use this formula to backtrack and determine the quantum state the electron was in before ionization. Calculating the principal quantum number from the given ionization energy shows us the initial state of the atom, a crucial insight for understanding atomic structure and behavior.