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 = 5. The frequency of the absorbed photon was __________ x 10^14 Hz.
9. Quantum Mechanics
Bohr Model
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The electron in a hydrogen atom absorbs a photon causing the electron to jump from the state n = 3 to the state n = 4. The frequency of the absorbed photon was __________ × 10¹⁴ Hz.
A
1.89
B
3.29
C
2.74
D
4.57
Verified step by step guidance1
Identify the initial and final energy levels of the electron in the hydrogen atom: n_initial = 3 and n_final = 4.
Use the Rydberg formula to calculate the energy difference between these two levels: E = -R_H * (1/n_final^2 - 1/n_initial^2), where R_H is the Rydberg constant for hydrogen (approximately 2.18 × 10^-18 J).
Calculate the energy difference (ΔE) using the values of n_initial and n_final in the Rydberg formula.
Relate the energy of the photon to its frequency using the equation E = h * ν, where h is Planck's constant (6.626 × 10^-34 J·s) and ν is the frequency of the photon.
Solve for the frequency (ν) by rearranging the equation to ν = ΔE / h, and substitute the calculated energy difference and Planck's constant to find the frequency of the absorbed photon.
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