it 163kJ/mol takes  to break an nitrogen-nitrogen single bond. Calculate the maximum wavelength of light for which an nitrogen-nitrogen single bond could be broken by absorbing a single photon.
Round your answer to  significant digits.

The energy required to break a bond can be related to the wavelength of light by using the following formula from quantum mechanics:

\[
E = \frac{hc}{\lambda}
\]

Where:
- \(E\) is the energy per photon,
- \(h\) is Planck's constant (\(6.626 \times 10^{-34} \, \text{J·s}\)),
- \(c\) is the speed of light (\(3.00 \times 10^8 \, \text{m/s}\)),
- \(\lambda\) is the wavelength of the photon.

Since the energy given is per mole, we need to first convert it to energy per photon. The conversion from kJ/mol to energy per photon is done by dividing by Avogadro's number (\(6.022 \times 10^{23} \, \text{mol}^{-1}\)):

1. Convert energy from kJ/mol to J/mol:
   \[
   163 \, \text{kJ/mol} = 163 \times 10^3 \, \text{J/mol}
   \]

2. Divide by Avogadro's number to get the energy per photon:
   \[
   E_{\text{photon}} = \frac{163 \times 10^3}{6.022 \times 10^{23}} \, \text{J}
   \]

Finally, rearrange the equation to solve for wavelength \(\lambda\):
\[
\lambda = \frac{hc}{E_{\text{photon}}}
\]

Let me calculate this.The maximum wavelength of light that can break a nitrogen-nitrogen single bond by absorbing a single photon is approximately **734 nm** (rounded to three significant digits).

Would you like more details or have any further questions?

Here are 5 related questions:
1. How does the energy of a photon relate to its frequency?
2. What is the significance of Planck's constant in quantum mechanics?
3. How does the bond energy of nitrogen differ between single, double, and triple bonds?
4. How can we experimentally determine the bond dissociation energy of molecules?
5. What are some real-world applications of photodissociation processes?

**Tip:** Shorter wavelengths of light carry higher energy photons, which can break stronger bonds.

It takes 163 kJ/mol to break a nitrogen-nitrogen single bond. Calculate the maximum wavelength of light for which a nitrogen-nitrogen single bond could be broken by absorbing a single photon. Round your answer to three significant digits.

Discover how to calculate the maximum wavelength of light needed to break a nitrogen-nitrogen single bond, using the bond energy of 163 kJ/mol. Learn the relationship between energy and wavelength using Planck's constant, the speed of light, and photon energy calculations. Suitable for undergraduate physics students.

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