Multiple Choice
A C–C bond has an average bond strength of 350 kJ/mol. What is the longest wavelength (lowest energy) light, in nm, that can break the average C–C bond? (1 m = 10⁹ nm)
9. Quantum Mechanics
Wavelength and Frequency
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Calculate the wavelength of light produced if an electron moves from n=5 state to n=3 state in a hydrogen atom. Use the Rydberg formula: 1/λ = R_H (1/n1² - 1/n2²), where R_H = 1.097 x 10^7 m^-1.
A
434 nm
B
486 nm
C
656 nm
D
1282 nm
Verified step by step guidance1
Identify the initial and final energy levels of the electron transition. Here, the electron moves from n=5 (initial state) to n=3 (final state).
Use the Rydberg formula to calculate the wavelength of light produced during the transition: \( \frac{1}{\lambda} = R_H \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right) \), where \( n_1 = 3 \) and \( n_2 = 5 \).
Substitute the known values into the Rydberg formula: \( R_H = 1.097 \times 10^7 \text{ m}^{-1} \), \( n_1 = 3 \), and \( n_2 = 5 \).
Calculate the difference in the inverse squares of the principal quantum numbers: \( \frac{1}{3^2} - \frac{1}{5^2} \).
Solve for \( \lambda \) by taking the reciprocal of the result from the Rydberg formula calculation to find the wavelength of the emitted light.
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