Question

The energy from radiation can be used to cause the rupture of chemical bonds. A minimum energy of \(941 \mathrm{~kJ} / \mathrm{mol}\) is required to break the nitrogen-nitrogen bond in \(\mathrm{N}_{2}\). What is the longest wavelength of radiation that possesses the necessary energy to break the bond? What type of electromagnetic radiation is this?

Short answer

The longest wavelength of radiation that can break the N-N bond in N2 molecule is \( 1273 \mathrm{nm} \), and it is Infrared radiation.

Step-by-step solution

Convert bond energy to joules per photon

As the given energy is in kJ/mol, we need to convert it into joules per photon. Since we know there are Avogadro's number (6.022 x 10^23) of photons in one mole, we'll divide the bond energy by Avogadro's number. Energy per mol = 941 kJ/mol = 941 x 10^3 J/mol Now, divide this by Avogadro's number to get the energy per photon: Energy per photon = \( \frac{941 \times 10^3 \mathrm{J/mol} }{ 6.022 \times 10^{23} \mathrm{mol^{-1}}} = 1.563 \times 10^{-19} \mathrm{J} \)

Use Planck's equation to find frequency

Planck's equation is \( E = h\nu \), where E is the energy, h is Planck's constant (6.626 x 10^-34 J s), and \( \nu \) is the frequency. To find the frequency, divide the energy per photon by Planck's constant : \( \nu = \frac{E}{h} \) \( \nu = \frac{1.563 \times 10^{-19} \mathrm{J}}{6.626 \times 10^{-34} \mathrm{J} \cdot \mathrm{s}} = 2.358 \times 10^{14} \mathrm{s}^{-1} \)

Use the speed of light equation to find the wavelength

The speed of light equation is \( c = \lambda\nu \), where c is the speed of light (3 x 10^8 m/s), \( \lambda\) is the wavelength, and \( \nu \) is the frequency. To find the wavelength, divide the speed of light by the frequency: \( \lambda = \frac{c}{\nu} \) \( \lambda = \frac{3 \times 10^8 \mathrm{m/s}}{2.358 \times 10^{14} \mathrm{s}^{-1}} = 1.273 \times 10^{-6} \mathrm{m} = 1273 \mathrm{nm} \)

Determine the type of electromagnetic radiation

Compare the wavelength to the range of wavelengths for each type of electromagnetic radiation: - Infrared: 700 nm to 1 mm - Visible: 400 nm to 700 nm - Ultraviolet: 10 nm to 400 nm Since the wavelength is within the infrared range, the radiation type is Infrared. Therefore, the longest wavelength of radiation that can break the N-N bond in N2 molecule is 1273 nm, and it is Infrared radiation.