Change in Potential Energy of an Electron in Hydrogen Atom

Explanation

When an electron in a hydrogen atom jumps from a higher energy level to a lower energy level, it releases energy in the form of electromagnetic radiation, such as a photon. This process is known as emission.

The energy of an electron in a hydrogen atom is given by the formula:

E = -(13.6 eV) / n^2

where E is the energy of the electron, n is the principal quantum number (1, 2, 3, etc.), and eV is electron-volts, a unit of energy.

When an electron moves from a higher energy level to a lower energy level, its energy decreases. The change in potential energy of the electron can be calculated using the formula:

ΔE = E2 - E1

where ΔE is the change in potential energy, E2 is the energy of the electron in the final (lower) energy level, and E1 is the energy of the electron in the initial (higher) energy level.

Calculation

In this case, the electron is moving from the third energy level (n=3) to the first energy level (n=1).

The energy of the electron in the third energy level is:

E3 = -(13.6 eV) / 3^2 = -1.51 eV

The energy of the electron in the first energy level is:

E1 = -(13.6 eV) / 1^2 = -13.6 eV

The change in potential energy of the electron is:

ΔE = E2 - E1 = (-13.6 eV) - (-1.51 eV) = -12.09 eV

Therefore, the change in potential energy of the electron is -12.09 eV. This means that the electron has released 12.09 eV of energy in the form of a photon as it moved from the third energy level to the first energy level.

Potential energy of an Orbit is two times the total energy

so energy of 1st orbit is -28.2 eV
3rd orbit is - 28.2 eV (1/3²) = -3.1 eV


so the potential energy difference is -25.1 eV