Determine the ionization energy required to extract the electron totally out of a hydrogen atom, and put it at rest
To determine the ionization energy required to completely remove an electron from a hydrogen atom and bring it to rest, we can refer to the energy level diagrams and atomic structure of hydrogen.
The ionization energy is defined as the energy required to remove an electron from an atom or molecule in its ground state. In the case of a hydrogen atom, the ground state corresponds to the electron being in the lowest energy level, which is the n=1 energy level.
The energy of an electron in a hydrogen atom can be calculated using the Rydberg formula:
E = -13.6 eV/n^2
Where E represents the energy of the electron, -13.6 eV is the ionization energy of hydrogen, and n is the principal quantum number representing the energy level.
Since we want to determine the ionization energy required to completely remove the electron and bring it to rest, we need to calculate the energy difference between the n=1 level and the energy at infinity (when the electron is at rest).
When the electron is at rest and far away from the nucleus, the energy approaches zero. So, we can set E = 0 and solve for n in the Rydberg formula:
0 = -13.6 eV/n^2
Rearranging the formula:
n^2 = -13.6 eV/0
As division by zero is undefined, the equation cannot be solved for a specific value of n. This implies that it would require an infinite amount of energy to bring the electron to rest infinitely far away from the nucleus.
Therefore, the ionization energy to completely remove the electron from a hydrogen atom and bring it to rest is infinite.