1. Calculate the Total Energy Emitted ($E_{\text{total}}$): Power ($P$) is energy per unit time ($P = E/t$). Given $P = 1 \text{ mW} = 1 \times 10^{-3} \text{ J s}^{-1}$ and time $t = 0.1 \text{ s}$. $E_{\text{total}} = P \times t = (1 \times 10^{-3} \text{ J s}^{-1}) \times (0.1 \text{ s}) = 1 \times 10^{-4} \text{ J}$

2. Calculate the Energy of One Photon ($E_{\text{photon}}$): Using the Planck equation $E = \frac{hc}{\lambda}$: Given $\lambda = 1000 \text{ nm} = 1000 \times 10^{-9} \text{ m} = 10^{-6} \text{ m}$. $E_{\text{photon}} = \frac{(6.626 \times 10^{-34} \text{ J s})(3 \times 10^8 \text{ m s}^{-1})}{10^{-6} \text{ m}}$ $E_{\text{photon}} = \frac{19.878 \times 10^{-26}}{10^{-6}} \text{ J} \approx 1.988 \times 10^{-19} \text{ J}$

3. Calculate the Number of Photons ($N$): $N = \frac{E_{\text{total}}}{E_{\text{photon}}} = \frac{1 \times 10^{-4} \text{ J}}{1.988 \times 10^{-19} \text{ J}}$ $N \approx 0.503 \times 10^{15} = 5.03 \times 10^{14}$

The value is closest to $5 \times 10^{14}$.