Multiple Choice
According to the Bohr theory of the hydrogen atom, what is the minimum energy (in J) needed to ionize a hydrogen atom from the n=2 state?
9. Quantum Mechanics
Bohr Model
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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.
A
n = 5
B
n = 6
C
n = 4
D
n = 3
Verified step by step guidance1
Identify the initial energy level of the electron, which is n = 2.
Use the formula for the energy of a photon: E = h * ν, where h is Planck's constant (6.626 × 10^-34 J·s) and ν is the frequency of the photon (4.57 × 10^14 Hz).
Calculate the energy of the absorbed photon using the given frequency.
Apply the Rydberg formula for hydrogen to find the change in energy levels: ΔE = -R_H * (1/n_f^2 - 1/n_i^2), where R_H is the Rydberg constant (2.18 × 10^-18 J), n_i is the initial energy level, and n_f is the final energy level.
Solve for the final energy level n_f by equating the energy of the photon to the change in energy levels and determine which of the given options (n = 3, n = 4, n = 5, n = 6) satisfies the equation.
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