Question

BIO 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?

Accepted Answer

Step 1: Calculate the energy of a single photon using the formula $$ E = \frac{hc}{\lambda} $$, where $$ h  is $$Planck's constant ($$ 6.626 	imes 10^{-34} \ 	ext{J·s} $$), $$ c  is $$the speed of light ($$ 3.00 	imes 10^8 \ 	ext{m/s} $$), and $$ \lambda  is $$the wavelength of the light (550 nm, which must be converted to meters: $$ 550 \ 	ext{nm} = 550 	imes 10^{-9} \ 	ext{m} ). $$Step 2: Calculate the total energy emitted by the firefly during one flash using the formula $$ E_{	ext{total}} = P \cdot t $$, where $$ P  is $$the power output (1.2 mW, which must be converted to watts: $$ 1.2 \ 	ext{mW} = 1.2 	imes 10^{-3} \ 	ext{W} ) $$and $$ t  is $$the duration of the flash (100 ms, which must be converted to seconds: $$ 100 \ 	ext{ms} = 0.1 \ 	ext{s} ). $$Step 3: Determine the number of photons emitted by dividing the total energy emitted by the energy of a single photon using the formula $$ N = \frac{E_{	ext{total}}}{E} $$, where $$ E  is $$the energy of a single photon (calculated in Step 1) and $$ E_{	ext{total}}  is $$the total energy emitted (calculated in Step 2). Step 4: Ensure all units are consistent throughout the calculations. For example, energy should be in joules, time in seconds, and wavelength in meters. This ensures the calculations are dimensionally correct. Step 5: Perform the division from Step 3 to find the number of photons emitted. This will give the final result in terms of the number of photons.

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Key Concepts

Photon Energy

Power and Energy Relationship

Photon Emission Calculation