Question

What is the energy in joules of a mole of photons associated with visible light of wavelength 486 nm? (c = 3.00 × 108 m/s; h = 6.63 × 10–34 J • s; NA = 6.022 × 1023 moles–1)

Answer 1

Answer: The energy of a mole of photons is $2.46\times 10^{5}J$

Explanation:

The relation between energy and wavelength of light is given by Planck's equation, which is:

$E=\frac{N_Ahc}{\lambda}$

where,  

E = energy

h = Planck's constant  = $6.626\times 10^{-34}Js$

c = speed of light  = 3.0\times 10^8m/s

$N_A$ =  Avogadro's number = $6.022\times 10^{23}$

$\lambda$ = wavelength of photon = 486 nm = $486\times 10^{-9}m$     (Conversion factor:  $1m=10^9nm$ )

Putting values in above equation, we get:  

$E=\frac{6.022\times 10^{23}\times 6.626\times 10^{-34}Js\times 3.0\times 10^8m/s}{486\times 10^{-9}m}\\\\E=2.46\times 10^{5}J/mol$

Hence, the energy of a mole of photons is $2.46\times 10^{5}J$