Question

Which of these transitions results in a photon with the shortest wavelength?

a) n = 3 to n = 1
b) n = 4 to n = 2
c) n = 5 to n = 3
d) n = 6 to n = 4

Answer 1

The transition from n = 3 to n = 1 results in a photon with the shortest wavelength.

Step-by-step explanation:

The transition that results in a photon with the shortest wavelength is from n = 3 to n = 1 (option a).

The wavelength of a photon is inversely proportional to its energy. The energy of a photon is given by the formula E = (hc)/λ, where h is Planck's constant, c is the speed of light, and λ is the wavelength. Since a photon with a shorter wavelength has higher energy, the transition with the shortest wavelength will have the highest energy. In this case, the transition from n = 3 to n = 1 involves a larger energy difference compared to the other transitions, resulting in a photon with the shortest wavelength.

To further illustrate, let's compare the energy differences for each transition:

• n = 3 to n = 1: ΔE = E3 - E1
• n = 4 to n = 2: ΔE = E4 - E2
• n = 5 to n = 3: ΔE = E5 - E3
• n = 6 to n = 4: ΔE = E6 - E4

Since the energy differences decrease as the transition goes from option a to option d, the transition from n = 3 to n = 1 (option a) will have the highest energy and therefore the shortest wavelength.