Chapter 6: Q2E (page 1275)

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 singlephoton 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.

Expert verified

The photon’s frequency, energy and velocity are $5.94 \times 10^{14} H z, 2.46 e V, 9.1 m m / s$ respectively.

Step by step solution

The frequency of a photon is,

$f = \frac{c}{λ}$

Substitute $c = 3 \times 10^{8} m / s a n d λ = 505 \times 10^{- 9} m$

$f = \frac{3 \times 10^{8} m / s}{505 \times 10^{- 9} m} = 5.94 \times 10^{14} m$

The energy of a photon is,

E = hf

Substitute $h = 6.626 \times 10^{- 34} J \cdot s a n d f = 5.94 \times 10^{14} H z$

$E = (6.626 \times 10^{- 34} J \cdot s) (5.94 \times 10^{14} H z) = 3.04 \times 10^{- 19} J = 2.46 e V$

The kinetic energy of the photon is,

$K = \frac{1}{2} m v^{2}$

Solve for the velocity,

$v = \sqrt{\frac{2 K}{m}}$

Substitute all the values in above equation,

$v = \sqrt{\frac{2 (3.94 \times 10^{- 19} J)}{9.5 \times 10^{- 15} k g}} = 9.1 m m / s$

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