11. Light is important in biology for photosynthesis. There are two different ways that light is described in physics.

In the first description, light travels in waves at a fixed speed c = 2.998 x 108 meters per second. The wavelength is the distance from peak to peak of a light wave, and corresponds to the color of the light. The wavelength is given by λ (the Greek letter lambda). The wavelength varies from 400 nm to 700 nm for light in the visible range, with blue light having λ=450 nm and red light having λ=680 nm.

The frequency is given by ν (the Greek letter nu). The frequency is the number of peaks that pass a point in a given time. Frequency is related to wavelength by the formula: ν = c / λ

In the second description, light travels in particles called photons or quanta. Using this description it makes sense to speak of a mole of light as 6.02 x 1023 photons.

The energy of one photon of light is given by

E = (hc) / λ = hν

where h is a conversion factor called Planck's constant; h = 1.583 x 10-34 calorie seconds.

In the laboratory, light with a very narrow wavelength range can be used for experiments. One mole of an actinic light (activating light) that has a wavelength of 680 nm was used to excite chlorophyll, and caused fluorescence measured at a wavelength of 690 nm. The chlorophyll was isolated, and therefore could do no photochemistry.

a. What is the amount of energy (in kilocalories) in one mole of actinic red light?

b. What is the amount of energy (in kcal) in the light that was fluoresced (assuming maximal fluorescence)?

c. What is the amount of energy (in kcal) that was lost as heat?

d. What percentage of the red light energy was lost as heat?

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