Whether the molecules of red or blue cones have longer box.

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Chapter 28, Problem 26CQ

To determine

Whether the molecules of red or blue cones have longer box.

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The molecules in the rods and cones in the eye are tuned to absorb photons of particular energies. The retinal molecule, like many molecules, is a long chain. Electrons can freely move along one stretch of the chain but are reflected at the ends, thus behaving like a particle in a one-dimensional box. The absorption of a photon lifts an electron from the ground state into the first excited state. Do the molecules in a red cone (which are tuned to absorb red light) or the molecules in a blue cone (tuned to absorb blue light) have a longer “box”?

The photoelectric equation for the kinetic energy of a photoelectron is, following Einstein, E < hf – W, where h is Planck's constant, f is the frequency of the light, and W is the work-function. Sodium has W = 3.2×10-19 J. When sodium is illuminated by monochromatic light of a particular frequency, electrons are emitted with speeds up to 8 x 105 ms-1. a) Calculate the wavelength of the light. b) Calculate the stopping potential.