The Change in Orbital Angular Momentum of a Hydrogen Atom

When a hydrogen atom emits a photon of energy 12.09 eV, its orbital angular momentum changes. To understand this phenomenon, we need to explore the principles of quantum mechanics and the behavior of electrons in atoms.

1. Quantum Mechanics
Quantum mechanics is a branch of physics that describes the behavior of particles at the atomic and subatomic levels. It provides a framework for understanding the properties and interactions of matter and energy.

2. Energy Levels in Hydrogen Atom
In a hydrogen atom, the electron revolves around the nucleus in specific energy levels or orbitals. These energy levels are characterized by their principal quantum number, n, which determines the size and energy of the orbit.

3. Emission of Photons
When an electron transitions from a higher energy level to a lower one, it releases energy in the form of a photon. The energy of the emitted photon is equal to the difference in energy between the initial and final states of the electron.

4. Orbital Angular Momentum
The orbital angular momentum of an electron is a property that describes the rotational motion of the electron around the nucleus. It is quantized and depends on the principal quantum number, n, and the azimuthal quantum number, l.

5. Change in Orbital Angular Momentum
When a hydrogen atom emits a photon, the electron transitions from a higher energy level to a lower one. This transition leads to a change in the orbital angular momentum of the electron.

6. Calculation of the Change in Orbital Angular Momentum
To calculate the change in orbital angular momentum, we need to consider the initial and final states of the electron. The orbital angular momentum is given by the formula:

L = ħ√(l(l+1))

where ħ is the reduced Planck's constant and l is the azimuthal quantum number.

The change in orbital angular momentum can be obtained by subtracting the initial orbital angular momentum from the final orbital angular momentum.

ΔL = L_final - L_initial

7. Conclusion
In conclusion, when a hydrogen atom emits a photon of energy 12.09 eV, its orbital angular momentum changes. This change is a result of the transition of the electron from a higher energy level to a lower one. The calculation of the change in orbital angular momentum involves considering the initial and final states of the electron and applying the formula for orbital angular momentum.