Question

In: Chemistry

Determine the energy of 1.80 mol of photons for each of the following kinds of light....

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 )

Solutions

Expert Solution

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


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