Physics
Physics
Problem
A hydrogen atom is excited to a higher energy level and then allowed to return to lower levels. (a) Explain with reason why photons are emitted only when the electron makes a downward transition between two permitted energy levels. (b) An electron is initially in the third energy level (). List all the distinct downward transitions that can occur until the electron finally reaches the ground state. (c) Using the list obtained in part (b), show how many different spectral lines can be observed for this case, and give a brief reason why no additional lines are possible once the electron reaches the first level. a. (i) Explain with reason why photons are emitted only when the electron makes a downward transition between two permitted energy levels. b. (ii) An electron is initially in the third energy level (). List all the distinct downward transitions that can occur until the electron finally reaches the ground state. c. (iii) Using the list obtained in part (ii), show how many different spectral lines can be observed for this case, and give a brief reason why no additional lines are possible once the electron reaches the first level.Intuitive explanation
The key to this problem is understanding that energy is quantized in atoms—electrons can only occupy specific energy levels, and light is emitted only when an electron "jumps" between these allowed states. When an electron drops from a higher level to a lower one, it releases energy as a photon with a frequency determined by the energy difference: . The crucial insight is that transitions can happen directly (e.g., ) or through intermediate levels (e.g., ), and each unique pair of levels produces a distinct spectral line—so you need to count all possible transitions, not just the number of levels involved.
Intuitive explanation
The key to this problem is understanding that energy is quantized in atoms—electrons can only occupy specific energy levels, and light is emitted only when an electron "jumps" between these allowed states. When an electron drops from a higher level to a lower one, it releases energy as a photon with a frequency determined by the energy difference: . The crucial insight is that transitions can happen directly (e.g., ) or through intermediate levels (e.g., ), and each unique pair of levels produces a distinct spectral line—so you need to count all possible transitions, not just the number of levels involved.