Multiple Choice
Determine the final value of n in a hydrogen atom transition if the electron starts in n = 2 and the atom absorbs a photon of light with a frequency of 4.57 × 10^14 Hz.
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9. Quantum Mechanics
Bohr Model
Multiple Choice
The electron in a hydrogen atom absorbs a photon causing the electron to jump from the state n = 2 to the state n = 7. The frequency of the absorbed photon was __________ x 10^14 Hz.
A
6.17
B
7.89
C
3.29
D
4.57
Verified step by step guidance1
Identify the initial and final energy levels of the electron in the hydrogen atom: n_initial = 2 and n_final = 7.
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).
Calculate the energy difference (ΔE) using the given energy levels: ΔE = 2.18 x 10^-18 J * (1/2^2 - 1/7^2).
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).
Solve for the frequency (ν) and express it in the form of x 10^14 Hz to match the given answer choices.
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