Question

A firefly glows by the direct conversion of chemical energy into light. The process is known as chemi-luminescence. The light emitted by the firefly has its peak intensity at a wavelength of 550 nm.

(a) What is the minimum chemical energy, in eV, required to generate each photon?
(b) One molecule of ATP provides 0.3 eV of energy when metabolized in the cell. What is the minimum number of ATP molecules needed to produce one photon of 550 nm light?
(c) The flash of light from the firefly lasts 100 ms and has a power of 1.2 mW. How many photons are emitted in the flash?

Answer 1

(a) The minimum chemical energy required to generate each photon of 550 nm light is approximately **2.25 eV.**

(b) To produce one photon of 550 nm light, the minimum number of ATP molecules needed is approximately **7.5 ATP molecules.**

(c) In the flash lasting 100 ms with a power of 1.2 mW, approximately **7.2 x
`10^15 p`hotons** are emitted.

Step-by-step explanation:

(a) The energy of a photon can be calculated using the formula
`\(E = (hc)/(\lambda),\) where \(h\)` is Planck's constant,
`\(c\)` is the speed of light, and
`\(\lambda\)` is the wavelength. Substituting the values, the energy of a 550 nm photon is approximately 2.25 eV.

(b) To determine the number of ATP molecules needed, the total energy required is divided by the energy provided by one ATP molecule.
`\( \text{Number of ATP molecules} = \frac{\text{Total energy required}}{\text{Energy per ATP molecule}}.\)` Substituting the values, approximately 7.5 ATP molecules are needed.

(c) The total number of photons emitted can be calculated using the formula
`\( \text{Power} = \frac{\text{Energy emitted}}{\text{Time}}.\)`Rearranging the formula to solve for energy emitted, and then dividing by the energy of one photon, we find the total number of photons. Substituting the values, approximately
`\(7.2 * 10^(15)\)` photons are emitted in the flash.

In summary, the chemi-luminescence process in fireflies requires a minimum energy of 2.25 eV per photon, and to produce one photon of 550 nm light, around 7.5 ATP molecules are needed. In a flash lasting 100 ms with a power of 1.2 mW, approximately
`\(7.2 * 10^(15)\)`photons are emitted.