4.4 Boffin questions

Fantastic Voyage

In the American science fiction film Fantastic Voyage (20^th Century Fox, 1966), a team of scientists are miniaturised along with a special submarine. The process of miniaturisation involves shrinking individual atoms. They are then injected into the bloodstream of an invaluable scientist to clear a blood clot and save his life. At one point in the film, the team travels through the inner ear where one team member, played by Raquel Welch, gets tangled in hair cell cilia. Obviously, the film is pure fantasy, but it is worth thinking about the implications of being shrunk to microscopic size.

1. In the film Fantastic Voyage, the hair cell cilia are about the width of Raquel Welch’s arm. In reality hair cell cilia are about 0.2 µm in width. What is the wavelength range of visible light? What are the implications of this for her vision once miniaturised?
2. If the humans are miniaturised only by shrinking their atoms, then their mass stays the same while their volume decreases. By what factor does their density (mass/volume) change? One way to calculate this is to assume a starting mass of 1,000 kg m^–3. Volume will approximately decrease by (miniature height / normal height)³. Assume they start at 1.8 m and decrease to 3 µm. What are the implications of this density change?