Question

Determine the energy of 1.70 mol of photons for each of the following kinds of light. (Assume three significant figures.)

1.infrared radiation (1590 nm )

2. visible light (485 nm )

3.ultraviolet radiation (170 nm )

Answer 1

1)

Given:

lambda = 1.59*10^-6 m

Find energy of 1 photon first

use:

E = h*c/lambda

=(6.626*10^-34 J.s)*(3.0*10^8 m/s)/(1.59*10^-6 m)

= 1.25*10^-19 J

This is energy of 1 photon

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

= 1.25*10^-19*6.022*10^23 J/mol

= 7.529*10^4 J/mol

= 75.29 KJ/mol

for 1.70 mol,

E = 1.70 mol * 75.29 KJ/mol

= 128 KJ

Answer: 128 KJ

2)

Given:

lambda = 4.85*10^-7 m

Find energy of 1 photon first

use:

E = h*c/lambda

=(6.626*10^-34 J.s)*(3.0*10^8 m/s)/(4.85*10^-7 m)

= 4.099*10^-19 J

This is energy of 1 photon

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

= 4.099*10^-19*6.022*10^23 J/mol

= 2.468*10^5 J/mol

= 2.468*10^2 KJ/mol

for 1.70 mol,

E = 1.70 mol * 2.468*10^2 KJ/mol

= 420. KJ

Answer: 420. KJ

3)

Given:

lambda = 1.7*10^-7 m

Find energy of 1 photon first

use:

E = h*c/lambda

=(6.626*10^-34 J.s)*(3.0*10^8 m/s)/(1.7*10^-7 m)

= 1.169*10^-18 J

This is energy of 1 photon

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

= 1.169*10^-18*6.022*10^23 J/mol

= 7.041*10^5 J/mol

= 7.041*10^2 KJ/mol

for 1.70 mol,

E = 1.70 mol * 7.041*10^2 KJ/mol

= 1.20*10^3 KJ

Answer: 1.20*10^3 KJ