As electrons fall from high energy orbitals to lower orbitals, energy is released in the form of electromagnetic radiation. The farther the electron falls, the more energy is released. Which of the following electronic transitions would produce a wave with the lowest frequency? A an electron falling from the 6th to the 2nd energy level B an electron falling from the 3rd to the 2nd energy level C an electron falling from the 5th to the 2nd energy level D an electron jumping from the 1st to the 2nd energy level

Answer 1

The frequency of the electromagnetic radiation produced when an electron transitions between energy levels is directly related to the energy difference between those levels. According to the formula \( E = h \cdot f \) (where \( E \) is the energy difference between the levels, \( h \) is Planck's constant, and \( f \) is frequency), a larger energy difference corresponds to a higher frequency, while a smaller energy difference produces a lower frequency.

In this question, you need to analyze the given transitions:

A. an electron falling from the 6th to the 2nd energy level: This transition involves a larger energy difference than many of the others; thus, it would emit a higher frequency photon.

B. an electron falling from the 3rd to the 2nd energy level: This transition has a moderate energy difference.

C. an electron falling from the 5th to the 2nd energy level: This transition has a larger energy difference than transition B, but not as large as transition A.

D. an electron jumping from the 1st to the 2nd energy level: This transition has the smallest energy gap of the options provided.

Comparing these transitions, the smallest energy transition corresponds to transition D. Therefore, the transition that would produce a wave with the lowest frequency is:

D an electron jumping from the 1st to the 2nd energy level.