What is the energy in kJ/mol of infrared radiation with a wavelength of 1.51 × 10⁻⁶ m?

• A. 79.1 kJ/mol
• B. 104.6 kJ/mol
• C. 25.7 kJ/mol
• D. 52.3 kJ/mol

Answer: (A)

Verified step by step guidance

1. Start by understanding the relationship between energy and wavelength. The energy of a photon can be calculated using the formula: $E=\frac{hc}{\lambda }$, where $h$ is Planck's constant ($6.626\times 10⁻34J·s$), $c$ is the speed of light ($3.00\times 10⁸m/s$), and $\lambda$ is the wavelength.
2. Substitute the given wavelength into the formula. Here, $\lambda$ is $1.51\times 10⁻6m$. Plug this value into the equation: $E=\frac{6.626\times 10⁻34J·s\times 3.00\times 10⁸m/s}{1.51}$.
3. Calculate the energy per photon using the substituted values. This will give you the energy in joules per photon. Remember that the units of $E$ will be in joules since you are using SI units.
4. Convert the energy from joules per photon to kilojoules per mole. Use Avogadro's number ($6.022\times 10²³$ molecules/mol) to find the energy per mole: $E=\frac{E\times 6.022\times 10²³}{1000}$.
5. Compare the calculated energy in kJ/mol with the given options to determine the correct answer. The calculated value should match one of the provided choices.