i need help on chemistry it multiple choice question

Question

The figure shows different possible transitions of electrons as they move from higher energy states to lower energy states. Which transition will produce the spectrum line with the lowest wavelength in this element’s atomic spectrum?

1. D
2. A

1. B

1. C

Answer 1

The larger the transition between energy levels, the more energy is absorbed or emitted.

However, as we know from the relationship between energy and wavelength, they are inversely proportional. Thus, the larger the transition, the more energy there is being produced, and thus the smaller the wavelength is.

Thus, the arrow with the longest transition (or spectrum line) will produce the lowest wavelength. The answer here will be D.

Answer 2

We can evaluate this question based on the Rydberg equation: E ≈ 1 / λ = R (1/n_f² – 1/n_i²)

The greater the value in parenthesis (based on energy levels), the lower the wavelength.

A. n = 2 → n = 1 : E ≈ 1 / λ = R (1/1 – 1/4) = 0.75R

B. n = 4 → n = 2 : E ≈ 1 / λ = R (1/4 – 1/16) = 0.19R

C. n = 4 → n = 3 : E ≈ 1 / λ = R (1/9 – 1/16) = 0.06R

D. n = 4 → n = 1 : E ≈ 1 / λ = R (1/1 – 1/16) = 0.94R ––> greatest E, lowest λ

Based on this limited analysis, the answer is D.