What is the energy (in J) of a mole of photons that have a wavelength of 775 nm? (h = 6.626 × 10⁻³⁴ J • s and c = 3.00 × 10⁸ m/s)

Answer 1

E=hv

E=energy in J

h=plancks constant=6.626E-34 J*s

v=frequency=Hz (1/s)

C=lambda v

c=speed of light=3E8m/s

lambda=wavelength in m

v=frequency

1) solve for frequency:

wavelength 775nm (1m/1E9nm)=7.75E-7 m

c=lambda v

v= c / lambda

v=3E8 / (7.75E-7)

v=3.87E14 s^-

2) substitute frequency in to solve for energy of 1 photon

E=hv

E=(6.626E-34 J s)(3.87E14 s^-)

E=2.56 E-19 J / single photon

3) convert from energy of one photon to energy of one mole (6.02E23) photons

1 mol of photons = 6.02E23 photons

2.56 E-19 J / single photon (6.02E23 photons / 1 mol photons)=154407 J/mol of photons