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The Bohr model introduces the idea of quantized energy levels in atoms, vital for understanding atomic behavior. For the hydrogen atom, which is the simplest case, the energy for any electron in an orbit (quantum state) is calculated using the formula: \[ E_n = -\frac{13.6 \text{ eV}}{n^2} \]Here, \(E_n\) represents the energy, while \(n\) is a positive integer known as the principal quantum number.
This principal quantum number identifies the specific energy levels, with lower values of \(n\) indicating more stable, lower energy states. In our specific case, the electron transitions from the \(n=5\) level, which has a higher energy (less negative), to the \(n=2\) level, a more stable lower energy level.
- **Energy Level Calculation**: - For \(n=5\): \(E_5 = -0.544 \text{ eV}\) - For \(n=2\): \(E_2 = -3.4 \text{ eV}\)The difference in these energy levels is crucial. The energy is released as a photon when the electron falls from a higher to a lower energy state. This is a key concept in understanding atomic transitions.

Photon emission occurs when an electron transitions between different energy levels within an atom. In this process, the energy difference between the initial and final states is converted into a photon—a packet of electromagnetic radiation.
- **Energy of the Photon**: - Calculated as the difference between the energies of the two levels: \(\Delta E = 2.856 \text{ eV}\) for the transition from \(n=5\) to \(n=2\). - This energy is often converted from electron volts (eV) to joules for calculation purposes, using the conversion factor \(1 \text{ eV} = 1.602 \times 10^{-19} \text{ J}\).
- **Wavelength of the Photon**: - The relationship between energy \(E\), wavelength \(\lambda\), and the constants Planck's constant \(h\) and the speed of light \(c\) is given by the formula: \(E = \frac{hc}{\lambda}\). - Solving for \(\lambda\), this leads to a wavelength \(\lambda \approx 435 \text{ nm}\), placing the photon within the visible light spectrum.
Photon emission is integral to many applications, such as lasers and light bulbs, highlighting the practical importance of understanding photon energy and wavelength.

Angular momentum conservation is a fundamental principle in physics, stating that in a closed system, the total angular momentum remains constant unless acted upon by external forces. In the context of the Bohr model and atomic transitions, this principle also applies on the atomic scale where each electron is viewed as having an angular momentum quantized by the rule:\[ L = n\hbar \]Here, \(n\) is an integer and \(\hbar\) (the reduced Planck's constant) is a fundamental physical constant. When an electron transitions from an upper to a lower energy level, its angular momentum changes by a unit of \(\hbar\).
- **Angular Momentum of the Photon**: - The change in angular momentum \(\Delta L = \hbar\). - The transition from \(n=5\) to \(n=2\) results in a photon possessing angular momentum of \(\hbar\), conserving the overall angular momentum of the system.
Understanding angular momentum conservation helps explain numerous physical phenomena beyond just atomic physics, such as the behavior of celestial bodies and the mechanics of everyday rotating objects.