Question

light and matter begin date: 9/2/2025 12:01:00 am due date: 9/5/2025 11:59:00 pm end date: 9/8/2025 11:59:00 pm problem 25: (3% of assignment value) ranking the figure above illustrates an energy - level diagram for hydrogen, with several electron transitions indicated by arrows. arrange the letters corresponding to each transition in order of the emitted wavelength, from longest to shortest. (assume the spacing of the lines is an accurate indicator of their relative energy levels.) longest shortest grade summary deductions 2% potential 98% submissions attempt(s) remaining: 998 2% deduction per attempt detailed view 1 2%

Explanation:

Step1: Recall energy - wavelength relation

The energy of a photon is given by $E = h
u=\frac{hc}{\lambda}$, where $h$ is Planck's constant, $
u$ is the frequency, $c$ is the speed of light, and $\lambda$ is the wavelength. So, $\lambda=\frac{hc}{E}$, which means that the smaller the energy of the emitted photon (from an electron - transition), the longer the wavelength.

Step2: Analyze electron - transitions

The energy of an electron - transition in a hydrogen atom is $\Delta E=E_{i}-E_{f}$, where $E_{i}$ is the initial energy level and $E_{f}$ is the final energy level. The larger the difference in energy levels, the larger the energy of the emitted photon.

Step3: Rank the transitions

Looking at the energy - level diagram, transition A has the smallest energy difference between the initial and final levels, followed by B, C, D, E, and F has the largest energy difference.

Answer:

A, B, C, D, E, F