Which of the electron transitions represents absorption with the greatest frequency?

• A. n = 5 to n = 3
• B. n = 1 to n =3
• C. n = 2 to n = 4
• D. n = 6 to n = 7
• E. n = 4 to n = 5

Answer: (B)

Verified step by step guidance

1. Understand that electron transitions involve an electron moving between energy levels in an atom, and absorption occurs when an electron moves to a higher energy level.
2. Recall that the frequency of absorbed light is directly related to the energy difference between the two levels: \( \Delta E = h \nu \), where \( \Delta E \) is the energy difference, \( h \) is Planck's constant, and \( \nu \) is the frequency.
3. Calculate the energy difference for each transition using the formula \( \Delta E = -13.6 \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right) \) eV, where \( n_1 \) and \( n_2 \) are the principal quantum numbers of the initial and final states, respectively.
4. Compare the energy differences for each transition: \( n = 1 \) to \( n = 3 \), \( n = 2 \) to \( n = 4 \), \( n = 5 \) to \( n = 3 \), \( n = 6 \) to \( n = 7 \), and \( n = 4 \) to \( n = 5 \). The transition with the largest energy difference corresponds to the highest frequency.
5. Identify that the transition from \( n = 1 \) to \( n = 3 \) has the greatest energy difference, and therefore, the greatest frequency of absorption.