QuestionMay 10, 2025

9) Air is about 76% nitrogen by mass. Nitrogen is nonreactive because the triple bond in N_(2) is not easily broken. The bond energy of the N_(2) triple bond is 945kJmol-1 What is the corresponding wavelength (nm) of light needed to break this triple bond for one molecule? (assuming one photon interacts with only one molecule) A) 9.45times 10^5nm B) 326 nm C) 1.27times 10^5nm D) 0.157 nm E) 127 nm

9) Air is about 76% nitrogen by mass. Nitrogen is nonreactive because the triple bond in N_(2) is not easily broken. The bond energy of the N_(2) triple bond is 945kJmol-1 What is the corresponding wavelength (nm) of light needed to break this triple bond for one molecule? (assuming one photon interacts with only one molecule) A) 9.45times 10^5nm B) 326 nm C) 1.27times 10^5nm D) 0.157 nm E) 127 nm
9) Air is about 76% nitrogen by mass. Nitrogen is nonreactive because the triple bond in N_(2) is not easily broken. The bond energy of the N_(2) triple bond is 945kJmol-1 What is the corresponding wavelength (nm) of light needed to break this triple bond for one molecule? (assuming one photon interacts with only one molecule) A) 9.45times 10^5nm B) 326 nm C) 1.27times 10^5nm D) 0.157 nm E) 127 nm

Solution
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Answer

127 nm Explanation 1. Calculate energy per molecule Convert bond energy from kJ/mol to J/molecule: \frac{945 \times 10^3 \, J/mol}{6.022 \times 10^{23} \, molecules/mol}. 2. Use Planck's equation **E = \frac{hc}{\lambda}**; solve for \lambda: \lambda = \frac{hc}{E}, where h = 6.626 \times 10^{-34} \, J \cdot s, c = 3.00 \times 10^8 \, m/s. 3. Calculate wavelength in nm Substitute E from Step 1 into the formula and convert meters to nanometers by multiplying by 10^9.

Explanation

1. Calculate energy per molecule<br /> Convert bond energy from $kJ/mol$ to $J/molecule$: $\frac{945 \times 10^3 \, J/mol}{6.022 \times 10^{23} \, molecules/mol}$.<br /><br />2. Use Planck's equation<br /> **E = \frac{hc}{\lambda}**; solve for $\lambda$: $\lambda = \frac{hc}{E}$, where $h = 6.626 \times 10^{-34} \, J \cdot s$, $c = 3.00 \times 10^8 \, m/s$.<br /><br />3. Calculate wavelength in nm<br /> Substitute $E$ from Step 1 into the formula and convert meters to nanometers by multiplying by $10^9$.
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