Question

Determine the energy of 1.80 mol of photons for each of the following kinds of light. (Assume three significant figures.)

infrared radiation (1420 nm )

visible light (505 nm )

ultraviolet radiation (140 nm )

Answer 1

The relationship between energy of a single photon and its wavelength is given as:

E = h c / λ

where, E = energy per photon; h = plancks constant = 6.626x10^-34 J s

c = speed of light = 3.00x10⁸ m/s; λ = wavelength

1. For infrared light: 1450 nm = 1450 x 10^-9 m

Energy of one photon, E = h c / λ

E = 6.626x10^-34 x 3.00x10⁸ / 1450 x 10^-9

E = 1.37 x 10^-19J

Now, energy of 1.80 mole of IR photons, E = 1.37 x 10^-19 x 1.80 x 6.022 x 10²³        

E = 1.48 x 10⁵ J

2. visible light: 505 nm = 505 x 10^-9 m

Energy of one photon, E = h c / λ

E = 6.626x10^-34 x 3.00x10⁸ / 505 x 10^-9

E = 3.93 x 10^-19J

Now, energy of 1.80 mole of visible light photons, E = 3.93 x 10^-19 x 1.80 x 6.022 x 10²³        

E = 4.25 x 10⁵ J

3. ultraviolet radiation: 140 nm = 140 x 10^-9 m

Energy of one photon, E = h c / λ

E = 6.626x10^-34 x 3.00x10⁸ / 140 x 10^-9

E = 1.41 x 10^-18J

Now, energy of 1.80 mole of visible light photons, E = 1.41 x 10^-18 x 1.80 x 6.022 x 10²³        

E = 1.52 x 10⁶ J