Light relationships

Question

What is the energy of 1.62 x 10^–3 moles of 4.77 nm X-ray photons?  in kJ

Answer 1

Given:

wavelength of photons = λ = 4.77 nm

moles of photons = 1.62x10^-3 mols

Asked for:

Energy of the photons

Calculations

First, convert 4.77 nm to m to be consistent with units of the speed of light (c)

4.77 nm x 10^-9 nm / m = 4.77x10^-9 m

Next, use the equation E = hc / λ

E = energy of 1 photon = ?

h = Planks constant = 6.626x10^-34 J-sec

c = speed of light = 3x10⁸ m / sec

λ = wavelength = 4.77x10^-9 m

E = (6.626x10^-34 J-sec)(3x10⁸ m / sec) / 4.77x10^-9 m

E = 4.17x10^-17 J / photon

Finally, use this value to find the total energy for 1.62x10^-3 photons and convert to the requested kJ

4.17x10^-17 J / photon x 1.62x10^-3 photons = 6.75x10^-20 J

6.75x10^-20 J x 1 kJ / 1000 J = 6.75x10^-23 kJ