Question

The wavelengths of light emitted by a firefly span the visible spectrum but have maximum intensity near 550 nm. A typical flash lasts for 100 ms and has a power output of 1.2 mW. How many photons does a firefly emit in one flash if we assume that all light is emitted at the peak intensity wavelength of 550 nm?

Short answer

Number of photons emitted are$3.32\times {10}^{14}$.

Step-by-step solution

Step 1. Given information is :Maximum intensity of Light - 550 nmFlash lasts for 100 ms and Power output = 1.2 mW 

We need to find out the numbers of photons that the firefly emits in one flash.

Step 2. Using the definition of Power.

$$\begin{gathered} P=\frac{E_{net}}{t} \\ {E}_{net}=N{E}_{photon} \\ {E}_{photon}=\frac{hc}{\lambda } \\ P=\frac{Nhc}{\lambda t} \\ N=\frac{P\lambda t}{hc} \\ N=\frac{\left(1.2\times {10}^{-3}W\right)\left(550\times {10}^{-9}m\right)\left(100\times {10}^{-3}s\right)}{\left(6.63\times {10}^{-34}\right)\left(3\times {10}^{8}m/s\right)} \\ N=3.32\times {10}^{14} \end{gathered}$$