Atomic Structure

In the hydrogen atom, the energy of the electron is quantized and can be given by: where is the principal quantum number, and is the ground state energy of hydrogen. To excite the electron, we need to provide energy equal to or greater than the energy difference between the levels. The maximum wavelength corresponds to the minimum energy needed for excitation. The energy and wavelength of a photon are related by: where is Planck's constant and is the speed of light. Solving for wavelength, we get: Thus, the maximum wavelength corresponds to the energy required to excite the hydrogen atom, and the formula is .

Concept:
Physics - Bohr's Atomic Model.
The energy of an electron in the orbit of a hydrogen atom is given by , where is the ground state energy.
Step 1: Identify the principal quantum number (n).

• Ground state:
• First excited state:
• Second excited state:

Step 2: Apply the energy formula.
Given eV and : $ $