객관식
Which of the following occurs as the wavelength of a photon increases?
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9. Quantum Mechanics
Wavelength and Frequency
객관식
Which of the following wavelengths corresponds to the longest wavelength of radiation that has enough energy to break a carbon-carbon single bond (bond energy ≈ 348 kJ/mol)?
A
210 nm
B
344 nm
C
120 nm
D
500 nm
검증된 단계별 안내1
Understand that the problem asks for the longest wavelength of radiation that can break a carbon-carbon single bond, which means the radiation must have at least the bond dissociation energy (348 kJ/mol).
Recall the relationship between energy and wavelength of electromagnetic radiation: \(E = \frac{hc}{\lambda}\), where \(E\) is the energy of one photon, \(h\) is Planck's constant, \(c\) is the speed of light, and \(\lambda\) is the wavelength.
Convert the bond energy from kJ/mol to energy per photon by dividing by Avogadro's number: \(E_{photon} = \frac{348 \times 10^3 \text{ J/mol}}{6.022 \times 10^{23} \text{ mol}^{-1}}\).
Rearrange the equation to solve for the wavelength: \(\lambda = \frac{hc}{E_{photon}}\).
Calculate \(\lambda\) using the constants \(h = 6.626 \times 10^{-34} \text{ J}\cdot\text{s}\) and \(c = 3.00 \times 10^8 \text{ m/s}\), then compare the calculated wavelength to the given options to identify the longest wavelength that has enough energy to break the bond.
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