The ground state energy of an oscillating electron is 1.23 eV. How much energy must be added to the electron to move it to the third excited state? The fourth excited state?

The energy that must be added to the electron to move it to the third excited state is - 1.153 eV The energy that must be added to the electron to move it to the fourth excited state is - 1.181 eV

Explanation:

Given;

Energy of electron in ground state (n = 1) = 1.23 eV

E₁ = 1.23 eV

Eₙ = E₁ / n²

where;

E₁ is the energy of the electron in ground state

n is the energy level,

For third excited state, n = 4

E₄ = E₁ / 4²

E₄ = (1.23 eV) / 16

E₄ = 0.077 eV

Change in energy level, = E₄ - E₁ = 0.077 eV - 1.23 eV = - 1.153 eV

The energy that must be added to the electron to move it to the third excited state is - 1.153 eV

For fourth excited state, n = 5

E₅ = E₁ / 5²

E₄ = (1.23 eV) / 25

E₄ = 0.049 eV

Change in energy level, = E₅ - E₁ = 0.049 eV - 1.23 eV = - 1.181 eV

The energy that must be added to the electron to move it to the fourth excited state is - 1.181 eV