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.1.What is the frequency of this photon?2.How much energy (in joules and eV ) does it deliver to the receptor cells?

Answer 1

1. $5.94\cdot 10^{14} Hz$

The frequency of a photon is given by:

$f=\frac{c}{\lambda}$

where

c is the speed of light

$\lambda$ is the wavelength

The wavelength of the photon in this problem is

$\lambda=505 nm=5.05\cdot 10^{-7}m$

So, the frequency of the photon is

$f=\frac{3\cdot 10^8 m/s}{5.05\cdot 10^{-7} m}=5.94\cdot 10^{14} Hz$

2. $3.94\cdot 10^{-19}J, 2.46 eV$

The energy of a photon is given by

$E=hf$

where

h is the Planck constant

f is the frequency of the photon

The frequency of the photon in this problem is

$f=5.94\cdot 10^{14} Hz$

so its energy in Joules is

$E=(6.63\cdot 10^{-34}Js)(5.94\cdot 10^{14}Hz)=3.94\cdot 10^{-19}J$

And since

$1 eV = 1.6\cdot 10^{-19}J$

The energy in eV is

$E=\frac{3.94\cdot 10^{-19} J}{1.6\cdot 10^{-19}J/eV}=2.46 eV$