Multiple Choice
An electron in the n = 7 level of the hydrogen atom relaxes to a lower-energy level, emitting light of 397 nm. What is the value of n for the level to which the electron relaxed?
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 = 4
B
n = 3
C
n = 5
D
n = 6
Verified step by step guidance1
Understand that the problem involves an electron transition in a hydrogen atom, where the electron absorbs a photon and moves to a higher energy level.
Use the formula for the energy of a photon: E = h * ν, where E is the energy, 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 photon using the given frequency and Planck's constant. This will give you the energy absorbed by the electron.
Recall the formula for the energy levels of a hydrogen atom: E_n = -13.6 eV / n^2, where E_n is the energy of the level and n is the principal quantum number. Convert the photon energy from joules to electron volts if necessary.
Determine the final value of n by finding the energy level that matches the sum of the initial energy level (n = 2) and the energy of the absorbed photon. Compare the calculated energy with the energy levels for n = 3, n = 4, n = 5, and n = 6 to find the correct transition.
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