To calculate the energy of infrared radiation with a given wavelength (λ) in kilojoules per mole (kJ/mol), you can use the following equation:
E = (hc) / λ
Where:
E is the energy in joules (J)
h is Planck's constant (6.626 x 10^-34 J·s)
c is the speed of light (2.998 x 10^8 m/s)
λ is the wavelength in meters (m)
To convert the energy from joules to kilojoules, you divide the result by 1000.
Let's calculate the energy for infrared radiation with a wavelength of λ = 1.41×10^-6 m:
E = (6.626 x 10^-34 J·s * 2.998 x 10^8 m/s) / (1.41×10^-6 m)
E ≈ 1.41 x 10^-19 J
To convert this energy to kilojoules per mole, we need to consider Avogadro's number (6.022 x 10^23 mol^-1):
E (kJ/mol) = (1.41 x 10^-19 J) / (6.022 x 10^23 mol^-1) * (10^-3 kJ/J)
E (kJ/mol) ≈ 2.34 x 10^-43 kJ/mol
Therefore, the energy of infrared radiation with a wavelength of λ = 1.41×10^-6 m is approximately 2.34 x 10^-43 kJ/mol.