Calculate the energy required for ionization of electron from the ground state of hydrogen atom
To calculate the energy required for ionization of an electron from the ground state of a hydrogen atom, we can use the formula for the energy of an electron in a hydrogen atom:
E = -13.6 eV / n^2
Where E is 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 (n=1 for the ground state).
For ionization to occur, we need to find the energy difference between the ground state (n=1) and the ionized state (n=∞). The ionization energy will be the energy required to move the electron from the ground state to the ionized state, thus the difference will be:
ΔE = E(ionized state) - E(ground state)
Since the ionized state is when n=∞, we substitute n=∞ into the energy equation:
E(ionized state) = -13.6 eV / ∞^2 = 0 eV
The energy of the ionized state is zero, as the electron is completely removed from the hydrogen atom.
Now, we can calculate the energy required for ionization:
ΔE = 0 eV - (-13.6 eV / 1^2) = 13.6 eV
Therefore, the energy required for ionization of an electron from the ground state of a hydrogen atom is 13.6 eV.
To calculate the energy required for ionization of an electron from the ground state of a hydrogen atom, we can use the formula for the energy of a photon emitted or absorbed during a transition between energy levels:
E = -13.6 × (Z² / n²) eV
where:
E is the energy of the photon,
Z is the atomic number (for hydrogen, Z = 1),
and n is the principal quantum number of the energy level.
In the ground state of hydrogen, the electron is in the n = 1 energy level. To calculate the ionization energy, we need to find the energy of the photon for the transition from n = 1 to n = ∞.
Using these values in the formula, we have:
E = -13.6 × (1² / 1²) = -13.6 eV
Therefore, the energy required for ionization of an electron from the ground state of a hydrogen atom is 13.6 eV.