The electron in a hydrogen atom absorbs a photon, causing the electron to jump from the state n = 2 to the state n = 8. The frequency of the absorbed photon was __________ x 10^14 Hz.

• A. 3.08
• B. 4.57
• C. 7.29
• D. 6.17

Answer: (B)

Verified step by step guidance

1. Identify the initial and final energy levels of the electron in the hydrogen atom: n_initial = 2 and n_final = 8.
2. Use the Rydberg formula to calculate the change in energy (ΔE) when an electron transitions between two energy levels: ΔE = R_H * (1/n_initial^2 - 1/n_final^2), where R_H is the Rydberg constant (2.18 x 10^-18 J).
3. Calculate the energy difference (ΔE) using the given energy levels: ΔE = 2.18 x 10^-18 J * (1/2^2 - 1/8^2).
4. Convert the energy difference (ΔE) to frequency (ν) using the equation: ν = ΔE / h, where h is Planck's constant (6.626 x 10^-34 J·s).
5. Express the frequency in the form of x * 10^14 Hz by dividing the calculated frequency by 10^14 and rounding to the appropriate number of significant figures.