객관식
The electron in a hydrogen atom absorbs a photon, causing the electron to jump from the state n = 2 to the state n = 8. The frequency of the absorbed photon was __________ x 10^14 Hz.
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9. Quantum Mechanics
Bohr Model
객관식
In the hydrogen spectrum, what is the wavelength of the photon emitted when an electron transitions from n = 3 to n = 2 in the Bohr model?
A
656 nm
B
486 nm
C
434 nm
D
410 nm
검증된 단계별 안내1
Identify the initial and final energy levels of the electron transition: n_initial = 3 and n_final = 2.
Use the Rydberg formula to calculate the wavelength of the emitted photon: \( \frac{1}{\lambda} = R_H \left( \frac{1}{n_{final}^2} - \frac{1}{n_{initial}^2} \right) \), where \( R_H \) is the Rydberg constant \( 1.097 \times 10^7 \text{ m}^{-1} \).
Substitute the values of n_initial and n_final into the Rydberg formula: \( \frac{1}{\lambda} = 1.097 \times 10^7 \left( \frac{1}{2^2} - \frac{1}{3^2} \right) \).
Calculate the difference in the fractions: \( \frac{1}{4} - \frac{1}{9} \), and simplify the expression.
Solve for \( \lambda \) by taking the reciprocal of the result from the Rydberg formula calculation to find the wavelength of the emitted photon.
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