Question

1. Fireflies emit light across the visible spectrum, but the peak intensity of their emission is around a wavelength of 550 nm. So let’s make the approximation that all of the light emitted by a firefly has a wavelength of 550 nm. (a) A typical flash of light from a firefly lasts for about 100 ms and has a power of 1.2 mW. How many photons are emitted in each flash. (b) An “electron volt” (eV) is a unit of energy. It is the energy that an electron gains when it “falls through” a potential difference of 1.0 V. What is an electron volt, in Joules. (c) Energy is stored in a firefly’s body (just like in your body) in ATP molecules. The amount of energy provided by metabolizing one ATP molecule is 0.30 eV. How many ATP molecules does the firefly need to metabolize to emit one photon

Answer 1

Assuming the firefly emits wavelength 550nm, amount of energy emitted is

h being the Planck’s constant, c is the velocity of light and lambda denotes its wavelength

This is the energy emitted by a single photon of wavelength 550 nm.

a) A flash of light from a firefly lasts 100 ms and has a power 1.2 mW

Hence in each flash amount of energy produced is

This is the energy produced by all the photons in a flash.

Hence, the number of photons (of wavelength 550 nm) in each flash is

b) Amount of work done, or the energy gained by a particle of charge q when accelerated through a potential V is

When an electron falls through a potential difference of 1 V it gains 1 eV of energy i.e.,

c) Amount of energy produced by metabolizing 1 ATP molecule is 0.30 eV

Amount of energy produced by one photon is

Let n ATP molecules are to be metabolized.

Hence amount of energy obtained from metabolizing n ATP molecules must be equal to the amount of energy emitted by a single photon.

Hence 8 ATP molecules are required.