https://file.aiquickdraw.com/mathbot/file/1730316673612x1toa5rm.jpg

To solve this problem, let's calculate the maximum wavelength of light required to break a nitrogen-nitrogen bond with an energy of 163 kJ/mol. Here’s the step-by-step approach:

### Step 1: Convert Bond Energy from kJ/mol to J per Photon
1 mole of photons corresponds to Avogadro's number, \( N_A = 6.022 \times 10^{23} \) photons.

The energy required to break a single nitrogen-nitrogen bond is given as 163 kJ/mol, so:
\[
\text{Energy per photon} = \frac{163 \times 10^3 \, \text{J/mol}}{6.022 \times 10^{23} \, \text{photons/mol}}
\]
\[
\text{Energy per photon} = 2.707 \times 10^{-19} \, \text{J}
\]

### Step 2: Use the Energy-Wavelength Relationship
The energy of a photon \( E \) is related to its wavelength \( \lambda \) by the equation:
\[
E = \frac{hc}{\lambda}
\]
where:
- \( h = 6.626 \times 10^{-34} \, \text{J} \cdot \text{s} \) (Planck's constant),
- \( c = 3.00 \times 10^8 \, \text{m/s} \) (speed of light).

Rearranging to solve for \( \lambda \):
\[
\lambda = \frac{hc}{E}
\]

### Step 3: Substitute Values
\[
\lambda = \frac{(6.626 \times 10^{-34}) \times (3.00 \times 10^8)}{2.707 \times 10^{-19}}
\]
\[
\lambda = 7.34 \times 10^{-7} \, \text{m} = 734 \, \text{nm}
\]

### Answer
The maximum wavelength of light required to break a nitrogen-nitrogen single bond is **734 nm**.

Would you like further details on any of the steps? 

---

**Follow-up questions:**
1. What is the relationship between photon energy and wavelength?
2. How would changing the bond energy affect the maximum wavelength?
3. Why is the energy of light important in chemical bond-breaking?
4. How can different types of bonds require different photon energies?
5. What happens if the photon energy is lower than required?

**Tip:** Remember, shorter wavelengths correspond to higher photon energies, which are necessary to break stronger bonds.

It takes 163. kJ/mol 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.

Explore how to calculate the maximum wavelength of light that can break a nitrogen-nitrogen single bond with an energy of 163 kJ/mol. This solution involves photon energy, wavelength calculation, and unit conversion using Planck's equation. Ideal for students in Grades 11-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation