If the potential energy of hydrogen electron is -3.02 eV then in which of the following excited level is electron present:

1. 1^st
2. 2^nd
3. 3^rd
4. 4^th

To determine the excited level of a hydrogen electron based on its potential energy of -3.02 eV, we need to understand how the energy levels of hydrogen are structured. The energy levels of a hydrogen atom can be calculated using the formula:

Energy Level Formula

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

E_n = -13.6 eV / n²

Here, E_n is the energy of the electron at level n, and n is the principal quantum number, which can take positive integer values (1, 2, 3, ...).

Calculating Energy Levels

Let’s calculate the energy for the first four energy levels:

• For n = 1: E₁ = -13.6 eV / 1² = -13.6 eV
• For n = 2: E₂ = -13.6 eV / 2² = -3.4 eV
• For n = 3: E₃ = -13.6 eV / 3² = -1.51 eV
• For n = 4: E₄ = -13.6 eV / 4² = -0.85 eV

Identifying the Excited State

Now, we compare the given potential energy of -3.02 eV with the calculated energy levels:

• E₁ = -13.6 eV
• E₂ = -3.4 eV
• E₃ = -1.51 eV
• E₄ = -0.85 eV

The potential energy of -3.02 eV falls between the energy levels of E₂ (-3.4 eV) and E₃ (-1.51 eV). Since -3.02 eV is closer to -3.4 eV, it indicates that the electron is in the second excited state, which corresponds to the principal quantum number n = 2.

Conclusion

Thus, the electron with a potential energy of -3.02 eV is present in the 2nd energy level of the hydrogen atom. This understanding of energy levels is crucial in quantum mechanics and helps explain the behavior of electrons in atoms.