Question

determine the energy of 1.80 mol of protons for each of the following kinds of light. (Assume three significant figures) visible light (515 nm), ultraviolet radiation (150 nm)

Answer 1

The relationships between the energy, frequency and wavelength are-

E = hv = hc/ƛ, where h = Planck’s constant =6.63e-34 J-s, c is the velocity of light =2.9979e8 m/s and ƛ is the wave length of visible light = 515 nm = 515e-9 m and for UV radiation = 150 nm = 150e-9 m

So, energy for 1 photon of visible light E_vis= (6.63e-34 J-s)*( 2.9979e8 m/s)/( 515e-9 m) =3.859e-19 J

For UV rad E_uv = (6.63e-34 J-s)*( 2.9979e8 m/s)/( 135e-9 m) =1.472e-18

1 mol photons = 6.023e23 (Avogadro’s number).

So, for 1.80 mol of photons will have energy for vis light =1.80*6.023e23*3.854e-19 J = 417827.556 J =4.18e5 J

And the same for UV light will be = 1.80*6.023e23*1.472e-18 J =1595854.08 = 1.595e6 J