The figure shows part of the energy level diagram of a certain atom. The energy spacing between levels 1 and 2 is twice that between 2 and 3. If an electron makes a transition from level 3 to level 2, the radiation of wavelength λ is emitted. What possible radiation wavelengths might be produced by other transitions between the three energy levels?
A) both λ/2 and λ/3
B) only λ/2
C) both 2λ and 3λ
D) only 2λ

Question

The figure shows part of the energy level diagram of a certain atom. The energy spacing between levels 1 and 2 is twice that between 2 and 3. If an electron makes a transition from level 3 to level 2, the radiation of wavelength λ is emitted. What possible radiation wavelengths might be produced by other transitions between the three energy levels? 
A) both λ/2 and λ/3 
B) only λ/2 
C) both 2λ and 3λ 
D) only 2λ

Quizplus · Accepted Answer

We know that the energy spacing between levels 1 and 2 is twice that between 2 and 3. Let's denote the energy spacing between levels 1 and 2 as E, and the energy spacing between levels 2 and 3 as E/2.

When an electron makes a transition from level 3 to level 2, it emits radiation of wavelength λ. This means that the energy difference between levels 3 and 2 is h*c/λ, where h is Planck's constant and c is the speed of light.

Since the energy spacing between levels 2 and 3 is E/2, the energy difference between levels 2 and 3 is E/2*h*c/λ. Similarly, the energy difference between levels 1 and 2 is E*h*c/λ.

Now we can consider the possible transitions between levels that could emit radiation. For example, if an electron were to make a transition from level 2 to level 1, it would emit radiation with energy E*h*c/λ. This corresponds to a wavelength of λ/2. Similarly, if an electron were to make a transition from level 3 to level 1, it would emit radiation with energy (E+E/2)*h*c/λ, which corresponds to a wavelength of λ/3.

Therefore, the possible radiation wavelengths that could be produced by other transitions between the three energy levels are λ/2 and λ/3. So the best choice is A) both λ/2 and λ/3.

The Figure Shows Part of the Energy Level Diagram of a Certain