Answer to Question #199500 in Mechanics | Relativity for Zaldy Manzo

Question

The human eye is most sensitive to green light of wavelength 505 nm. Experiments have found that when people are kept in a dark room until their eyes adapt to the darkness, a single photon of green light will trigger receptor cells in the rods of the retina. (a) What is the frequency of this photon? (b) How much energy (in joules and electron volts) does it deliver to the receptor cells? (c) To appreciate what a small amount of energy this is, calculate how fast a typical bacterium of mass 9.5 x 10-12 g would move if it had that much energy.

Answer 1

a) Frequency is calculate by this formula $\frac{c}{\lambda}=\frac{3\times10^8}{505\times10^{-9}}=5.94\times10^{14}Hz$

b) Energy =$hv=6.63\times10^{-34}\times5.94\times10^{14}=3.9\times10^{-19}J$

c) $3.9\times10^{-19}=1/2mv^2=1/2\times 9.5\times 10^{-15}v^2$

$v^2=\frac{3.9\times 10^{-19}}{0.5\times 9.5\times 10^{-15}}=8.21053\times 10^{-5}$

$v=\sqrt{8.21053\times 10^{-5}}=9.06\times 10^{-3}m/s$