CHEM-327 Lecture 12

Energy Levels for Particle in a 1D Box

$E_n = \frac{n^2h^2}{8mL^2}$, where $n$ is the principal quantum number, $h$ is Planck's constant, $m$ is the mass of the particle, and $L$ is the length of the box.

Energy Difference from Quantum Transition

For a transition between two energy levels ($n<em>f$ and $n</em>i$), the general energy difference is $\Delta E = E<em>{n</em>f} - E<em>{n</em>i}$. For $n=1$ to $n=2$ in a 1D box, $\Delta E = \frac{3h^2}{8mL^2}$.

Photon Energy and Wavelength Relationship

$\Delta E = h\nu = \frac{hc}{\lambda}$, where $\Delta E$ is the energy difference, $h$ is Planck's constant, $\nu$ is the frequency of the photon, $c$ is the speed of light, and $\lambda$ is the wavelength of the photon.

Wavelength for $n=1$ to $n=2$ Transition in a 1D Box

$\lambda = \frac{8mL^2c}{3h}$, calculated from the energy difference $\Delta E = \frac{3h^2}{8mL^2}$ and the photon energy equation.