Question

Determine the energy of 1.90 mol of photons for each of the following kinds of light. (Assume three significant figures.)

infrared radiation (1410 nm )

visible light (520 nm )

ultraviolet radiation (150 nm )

For all of them "E = ____ kJ"

Answer 1

1)

we have:

wavelength = 1.41*10^-6 m

Find energy of 1 photon first

we have:

wavelength = 1.41*10^-6 m

we have below equation to be used:

Energy = Planck constant*speed of light/wavelength

=(6.626*10^-34 J.s)*(3.0*10^8 m/s)/(1.41*10^-6 m)

= 1.41*10^-19 J

This is energy of 1 photon

Energy of 1 mol = energy of 1 photon * Avogadro's number

= 1.41*10^-19*6.022*10^23 J/mol

= 8.49*10^4 J/mol

= 84.9 KJ/mol

for 1.90 mol,

E = 1.90 mol * 84.9 KJ/mol

= 161 KJ

Answer: 161 KJ

2)

we have:

wavelength = 5.2*10^-7 m

Find energy of 1 photon first

we have:

wavelength = 5.2*10^-7 m

we have below equation to be used:

Energy = Planck constant*speed of light/wavelength

=(6.626*10^-34 J.s)*(3.0*10^8 m/s)/(5.2*10^-7 m)

= 3.823*10^-19 J

This is energy of 1 photon

Energy of 1 mol = energy of 1 photon * Avogadro's number

= 3.823*10^-19*6.022*10^23 J/mol

= 2.302*10^5 J/mol

= 230.2 KJ/mol

for 1.90 mol,

E = 1.90 mol * 230.2 KJ/mol

= 437 KJ

Answer: 437 KJ

3)

we have:

wavelength = 1.5*10^-7 m

Find energy of 1 photon first

we have:

wavelength = 1.5*10^-7 m

we have below equation to be used:

Energy = Planck constant*speed of light/wavelength

=(6.626*10^-34 J.s)*(3.0*10^8 m/s)/(1.5*10^-7 m)

= 1.325*10^-18 J

This is energy of 1 photon

Energy of 1 mol = energy of 1 photon * Avogadro's number

= 1.325*10^-18*6.022*10^23 J/mol

= 7.98*10^5 J/mol

= 798 KJ/mol

for 1.90 mol,

E = 1.90 mol * 798 KJ/mol

= 1516 KJ

Answer: 1516 KJ