Question

what is the energy of a mole of photons that have a wavelength of 695 nm? answer: j

Explanation:

Step1: Convert wavelength to meters

Given $\lambda = 695\ nm=695\times10^{- 9}\ m$.

Step2: Use the energy - wavelength formula for a single photon

The energy of a single photon is $E = h\frac{c}{\lambda}$, where $h = 6.626\times10^{-34}\ J\cdot s$ (Planck's constant) and $c = 3\times10^{8}\ m/s$ (speed of light). So $E=\frac{6.626\times10^{-34}\ J\cdot s\times3\times10^{8}\ m/s}{695\times10^{-9}\ m}\approx2.86\times10^{-19}\ J$.

Step3: Calculate the energy of a mole of photons

We know that 1 mole contains $N_A=6.022\times10^{23}$ photons. So the energy of a mole of photons $E_{mol}=N_A\times E$.
$E_{mol}=6.022\times10^{23}\times2.86\times10^{-19}\ J\approx172200\ J = 172.2\ kJ$.

Answer:

$172200$