Multiple Choice
At what speed must a 145-g baseball travel to have a wavelength of 1.15 × 10−34 m?
9. Quantum Mechanics
Wavelength and Frequency
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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)
A
3420 nm
B
342000 nm
C
34200 nm
D
342 nm
Verified step by step guidance1
Understand that the energy required to break a bond is related to the wavelength of light through the equation: \( E = \frac{hc}{\lambda} \), where \( E \) is the energy in joules, \( h \) is Planck's constant \( 6.626 \times 10^{-34} \text{ J s} \), \( c \) is the speed of light \( 3.00 \times 10^{8} \text{ m/s} \), and \( \lambda \) is the wavelength in meters.
Convert the bond energy from kJ/mol to J/molecule. Since 1 mol contains \( 6.022 \times 10^{23} \) molecules (Avogadro's number), the energy per molecule is \( \frac{350 \times 10^{3} \text{ J/mol}}{6.022 \times 10^{23} \text{ molecules/mol}} \).
Substitute the energy per molecule into the equation \( E = \frac{hc}{\lambda} \) to solve for \( \lambda \). Rearrange the equation to \( \lambda = \frac{hc}{E} \).
Calculate \( \lambda \) using the values for \( h \), \( c \), and the energy per molecule. Ensure that the units are consistent, with \( \lambda \) being calculated in meters.
Convert the wavelength from meters to nanometers by multiplying by \( 10^{9} \) (since \( 1 \text{ m} = 10^{9} \text{ nm} \)). This will give you the longest wavelength of light that can break the C–C bond.
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