Calculate The Wavelength of Light Required to Break

How to calculate the wavelength of light required to break a bond

The wavelength of light required to break a chemical bond is determined by the bond's energy. Higher energy bonds require shorter wavelengths of light to break. The calculation involves converting the bond energy from electron volts (eV) to joules, then using Planck's equation to find the wavelength.

Steps to calculate

1. Determine the bond energy in electron volts (eV). This value represents how much energy is required to break the bond.
2. Convert the bond energy from eV to joules using the conversion factor 1 eV = 1.60218 × 10⁻¹⁹ J.
3. Use Planck's equation to calculate the wavelength: λ = hc/E, where λ is the wavelength, h is Planck's constant (6.62607 × 10⁻³⁴ J·s), c is the speed of light (2.99792 × 10⁸ m/s), and E is the bond energy in joules.
4. The result is the minimum wavelength of light required to break the bond.

Key considerations

• The bond energy must be known or estimated for accurate results.
• The calculation assumes the photon energy equals the bond energy, which is a simplification.
• Different types of light (UV, visible, infrared) have different wavelength ranges that can be used to identify the light type needed.

Formula used

The bond energy must be converted from electron volts (eV) to joules using the conversion factor 1 eV = 1.60218 × 10⁻¹⁹ J.

Worked example

Let's calculate the wavelength of light required to break a bond with an energy of 5 eV.

Step 1: Convert bond energy to joules

5 eV × 1.60218 × 10⁻¹⁹ J/eV = 8.0109 × 10⁻¹⁹ J

Step 2: Calculate wavelength using Planck's equation

λ = (6.62607 × 10⁻³⁴ J·s × 2.99792 × 10⁸ m/s) / 8.0109 × 10⁻¹⁹ J

λ ≈ 2.47 × 10⁻⁷ meters

Step 3: Convert wavelength to nanometers

2.47 × 10⁻⁷ m × 10⁹ nm/m = 247 nm

The result is 247 nanometers, which is in the ultraviolet (UV) range. This means UV light with a wavelength of approximately 247 nm is required to break this bond.