Multiple Choice
According to the Bohr model, what is the wavelength of light emitted when an electron transitions from the n=2 to the n=1 energy level in a hydrogen atom?
9. Quantum Mechanics
Bohr Model
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Which of the following transitions (in a hydrogen atom) represent emission of the shortest wavelength?
A
n = 3 to n = 1
B
n = 2 to n = 4
C
n = 1 to n = 4
D
n = 5 to n = 3
E
n = 2 to n = 5
Verified step by step guidance1
Understand that the emission of light in a hydrogen atom occurs when an electron transitions from a higher energy level (n) to a lower energy level.
Recall that the energy difference between two levels is given by the Rydberg formula: \( E = R_H \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right) \), where \( R_H \) is the Rydberg constant, \( n_1 \) is the lower energy level, and \( n_2 \) is the higher energy level.
Recognize that the wavelength of the emitted light is inversely proportional to the energy difference: \( \lambda = \frac{hc}{E} \), where \( h \) is Planck's constant and \( c \) is the speed of light.
To find the transition with the shortest wavelength, identify the transition with the largest energy difference, as a larger energy difference corresponds to a shorter wavelength.
Calculate the energy differences for each transition using the Rydberg formula and compare them to determine which transition has the largest energy difference, thus the shortest wavelength.
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