Question

What is the wavelength, in nanometers, of light with an energy content of 1.59 x 10^5 kJ mol^(-1)? Hint: The unit mol^(-1) should be interpreted as "per mole of photons."

a) 384 nm
b) 458 nm
c) 502 nm
d) 615 nm

Answer 1

To calculate the wavelength of light, given its energy per mole, we convert the energy to joules per photon and use Planck's equation. The calculated wavelength in this case is 752.5 nm, which does not match any of the provided answer choices; suggesting an error in the calculations or question data.

Step-by-step explanation:

To find the wavelength of light in nanometers with a given energy content of 1.59 x 105 kJ mol-1, we can use the energy-wavelength relationship given by Planck's equation, which connects the energy of a photon (E) to its wavelength (λ) via Planck's constant (h) and the speed of light (c). The equation is E = hc/λ, or λ = hc/E. Given that Planck's constant (h) is 6.626 x 10-34 J s and the speed of light (c) is 3.00 x 108 m/s, we can convert the energy given in kJ to J (1 kJ = 103 J), and then solve for λ. To find the wavelength, first convert energy per mole to energy per photon by dividing by Avogadro's number (6.022 x 1023 mol-1).

The calculation will look as follows:

1. Convert the energy from kJ/mol to J/photon: 1.59 x 105 kJ mol-1 x 103 J/kJ = 1.59 x 108 J mol-1
2. Divide by Avogadro's number: 1.59 x 108 J mol-1 / 6.022 x 1023 mol-1 = 2.638 x 10-16 J/photon
3. Calculate the wavelength: λ = hc/E = (6.626 x 10-34 J s x 3.00 x 108 m/s) / 2.638 x 10-16 J = 752.5 x 10-9 m, which is 752.5 nm

However, none of the provided answer options (a) 384 nm, (b) 458 nm, (c) 502 nm, or (d) 615 nm matches the calculated wavelength of 752.5 nm. Therefore, it would be best to re-evaluate the calculations or provided information since there might be an error in either the given values or the answer choices.