A photon with wavelength λis absorbed by an electron confined to a box. As a result, the electro

step 1 So in this question we have an electron that is trapped confined in the box. So this, we usually

A photon with wavelength λis absorbed by an electron...

A photon with wavelength $\lambda$ is absorbed by an electron confined to a box. As a result, the electron moves from state $n=1$ to $n=4 .$ (a) Find the length of the box. (b) What is the wavelength of the photon emitted in the transition of that electron from the state $n=4$ to the state $n=2 ?$

Key Concepts

Particle in a Box Model

This model describes a quantum particle that is confined within an infinitely deep potential well, meaning that the particle is free to move inside a defined region but cannot exist outside it. The key outcome of this model is that the allowed energy states are quantized, and the particle’s behavior is governed by a wave function that must satisfy boundary conditions at the walls of the box.

Quantization of Energy Levels

In quantum mechanics, when a particle is confined to a finite region, its allowed energy levels are discrete rather than continuous. For a particle in a box, these energy levels depend on the quantum number and other constants such as the particle’s mass and the size of the box. Energy differences between these levels correspond to observable phenomena like absorption or emission of photons.

Photon Absorption and Emission

When an electron makes a transition between quantized energy states, it must absorb or emit a photon to conserve energy. Absorption occurs when the electron moves to a higher energy state while emitting a photon corresponds to a drop to a lower energy state. The energy of the photon is exactly equal to the difference in energy between the two states.

Photon Energy-Wavelength Relationship

The energy of a photon is inversely proportional to its wavelength, described by the equation E = hc/?, where h is Planck’s constant, c is the speed of light, and ? is the wavelength. This relationship is crucial for linking the energy differences between quantum states to measurable quantities like wavelength in spectroscopic transitions.

Transcript

Please give Ace some feedback