Question

How much energy (in kj) do 3.0 moles of photons, all with a wavelength of 670 nm, contain? how much energy (in kj) do 3.0 moles of photons, all with a wavelength of 670 nm, contain? 360 kj 179 kj 536 kj 242 kj 412 kj?

Answer 1

1 mole of photons contain $6.023 \cdot 10^{23}$ photons (Avogadro number). This means that 3.0 moles of photons contain
$N=3\cdot 6.023 \cdot 10^{23} =1.81 \cdot 10^{24}$ photons.

The wavelength of the light in the problem is $\lambda=670 nm=670\cdot 10^{-9}m$, so the frequency is
$f= \frac{c}{\lambda}= \frac{3\cdot 10^8 m/s}{670 \cdot 10^{-9}m}=4.48 \cdot 10^{14}Hz$

The energy carried by a single photon is
$E=hf$
where $h=6.62 \cdot 10^{-34}Js$ is the Planck constant, while f is the frequency. Since this is the energy carried by a single photon, the energy carried by 3.0 moles of photons will be the energy of the single photon multiplied by the total number of photons:
$E=Nhf=(1.81 \cdot 10^{24})(6.62 \cdot 10^{-34}Js)(4.48 \cdot 10^{14}Hz )=5.36 \cdot 10^5 J$
which corresponds to E=536 kJ.