Question

it takes 157. kj/mol to break a nitrogen-oxygen single bond. calculate the maximum wavelength of light for which a nitrogen-oxygen single bond could be broken by absorbing a single photon.
round your answer to 3 significant digits.

Explanation:

Step1: Calculate the energy per photon

The energy required to break one \(N - O\) bond is \(E=\frac{157\times10^{3}\text{ J/mol}}{6.022\times 10^{23}\text{ mol}^{-1}}\)

$$E=\frac{157000}{6.022\times 10^{23}}\text{ J}\approx2.607\times 10^{-19}\text{ J}$$

Step2: Use the formula \(E = h

u=\frac{hc}{\lambda}\) to find \(\lambda\)
We know that \(h = 6.626\times 10^{-34}\text{ J}\cdot\text{s}\) and \(c=3\times 10^{8}\text{ m/s}\)
From \(\lambda=\frac{hc}{E}\), substitute the values:
\(\lambda=\frac{6.626\times 10^{-34}\times3\times 10^{8}}{2.607\times 10^{-19}}\text{ m}\)

$$
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Convert meters to nanometers: \(\lambda = 763\text{ nm}\)

Answer:

\(763\)