The electron in a hydrogen atom absorbs a photon causing the electron to jump from the state n = 2 to the state n = 5. The frequency of the absorbed photon was __________ x 10^14 Hz.

• A. 7.12
• B. 3.29
• C. 6.17
• D. 4.57

Answer: (C)

Verified step by step guidance

1. Understand that the problem involves an electron transition in a hydrogen atom, which can be analyzed using the Rydberg formula for hydrogen: $\frac{-R\left(H^2\right)}{n^2}$, where $R$ is the Rydberg constant and $n$ is the principal quantum number.
2. Calculate the energy difference between the two states using the formula: $E=R(\frac{1}{n^2}-\frac{1}{n^2})$, where $n=2$ and $n=5$.
3. Convert the energy difference to frequency using the relation $E=hf$, where $h$ is Planck's constant and $f$ is the frequency.
4. Rearrange the formula to solve for frequency: $f=\frac{E}{h}$.
5. Substitute the calculated energy difference and Planck's constant into the equation to find the frequency of the absorbed photon.