The minimum energy required for an electron to escape from a hydrogen atom can be calculated using the formula for the ionization energy. The ionization energy represents the energy required to remove an electron from its bound state in an atom or molecule.
For a hydrogen atom, the ionization energy can be determined using the Rydberg formula:
E = -RH/n^2
where E is the ionization energy, RH is the Rydberg constant (approximately 13.6 electron volts), and n is the principal quantum number of the initial energy level of the electron.
In the case of the minimum energy required to escape from a hydrogen atom, the electron is in the ground state (n = 1) and needs to move to infinity (where its potential energy becomes zero). Therefore, the ionization energy can be calculated as follows:
E = -RH/1^2 = -13.6 eV
Thus, the minimum energy required for an electron to escape from a hydrogen atom is 13.6 electron volts (eV). It should be noted that this calculation assumes the hydrogen atom is in its ground state and neglects factors such as electron-electron interactions and relativistic effects, which can influence the precise energy values in more complex scenarios.