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.
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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 = 3 to the state n = 6. The frequency of the absorbed photon was __________ x 10^14 Hz.
A
2.74
B
6.23
C
4.57
D
8.91
Verified step by step guidance1
Understand that the problem involves an electron transition in a hydrogen atom, where the electron moves from an initial energy level (n = 3) to a higher energy level (n = 6) due to absorption of a photon.
Recall the formula for the energy difference between two levels in a hydrogen atom: , where is the Rydberg constant (approximately 2.18 x 10^-18 J), and and are the initial and final energy levels, respectively.
Calculate the energy difference using the formula: . This will give you the energy absorbed by the electron.
Use the relationship between energy and frequency of a photon: , where is Planck's constant (approximately 6.63 x 10^-34 J·s) and is the frequency. Rearrange to solve for frequency: .
Substitute the calculated energy difference and Planck's constant into the frequency formula to find the frequency of the absorbed photon. This will give you the frequency in Hz, which can be compared to the options provided.
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