Calculate the energy per mole of photon of electromagnetic radiation having wave length 700 nm $\left[\mathrm{h}=6.626 \times 10^{-34} \mathrm{Js}, \mathrm{C}=3 \times 10^8 \mathrm{~m} / \mathrm{s}\right]$

Energy per mole of photons is calculated from the energy of a single photon multiplied by Avogadro's number.

The energy of a photon is given by $E = \frac{hc}{\lambda}$, where Planck's constant $h = 6.626 \times 10^{-34} \mathrm{Js}$, the speed of light $c = 3 \times 10^8 \mathrm{m/s}$, and wavelength $\lambda = 700 \,\mathrm{nm} = 7 \times 10^{-7} \,\mathrm{m}$.

Substituting these values:
$E = \frac{(6.626 \times 10^{-34}) \cdot (3 \times 10^8)}{7 \times 10^{-7}} = 2.8397 \times 10^{-19} \,\mathrm{J}$.

Multiplying by Avogadro's number $N_{\mathrm{A}} = 6.022 \times 10^{23} \,\mathrm{mol}^{-1}$ gives the energy per mole:
$E_{\mathrm{mole}} = (2.8397 \times 10^{-19}) \cdot (6.022 \times 10^{23}) = 1.7109 \times 10^5 \,\mathrm{J/mol}$.

Rounded to three significant figures, the value is $1.71 \times 10^5 \,\mathrm{J/mol}$.

Among the options, A) $1.71 \times 10^5 \,\mathrm{J}$ matches this result.

$\boxed{\mathrm{A}}$