Which electron transition in the hydrogen atom produces light of the highest frequency?

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

Answer: (A)

Verified step by step guidance

1. Recall that the frequency of light emitted during an electron transition in a hydrogen atom is related to the energy difference between the two energy levels involved. The greater the energy difference, the higher the frequency of the emitted light.
2. Use the energy level formula for the hydrogen atom: \(E_n = -\frac{13.6\ \text{eV}}{n^2}\), where \(n\) is the principal quantum number of the energy level.
3. Calculate the energy difference \(\Delta E\) for each transition by subtracting the energy of the lower level from the energy of the higher level: \(\Delta E = E_{\text{initial}} - E_{\text{final}}\).
4. Since frequency \(\nu\) is related to energy by the equation \(\Delta E = h \nu\), where \(h\) is Planck's constant, the transition with the largest \(\Delta E\) will produce the highest frequency light.
5. Compare the energy differences for the given transitions (\(n=2 \to n=1\), \(n=3 \to n=2\), \(n=4 \to n=3\), \(n=5 \to n=4\)) to determine which one has the greatest \(\Delta E\) and thus the highest frequency.