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 in the order indicated. Separate your answers with a comma.3.To appreciate what a small amount of energy this is, calculate how fast a typical bacterium of mass 9.50�10?12 g would move if it had that much energy.

Answer 1

`5.94059* 10^(14)\ Hz`

`3.93623* 10^(-19)\ J\ or\ 2.456994766\ eV`

0.0091 m/s

Step-by-step explanation:

h = Planck's constant =
`6.626* 10^(-34)\ m^2kg/s`

c = Speed of light =
`3* 10^8\ m/s`

`\lambda` = Wavelength = 505 nm

m = Mass of bacterium =
`9.5* 10^(-15)\ kg`

Frequency is given by

`f=(c)/(\lambda)\\\Rightarrow f=(3* 10^8)/(505* 10^(-9))\\\Rightarrow f=5.94059* 10^(14)\ Hz`

Freqeuncy is
`5.94059* 10^(14)\ Hz`

Energy is given by

`E=hf\\\Rightarrow E=6.626* 10^(-34)* 5.94059* 10^(14)\\\Rightarrow E=3.93623* 10^(-19)\ J=3.93623* 10^(-19)* 6.242* 10^(18)\\\Rightarrow E=2.456994766\ eV`

Energy is
`3.93623* 10^(-19)\ J\ or\ 2.456994766\ eV`

The above energy is the kinetic energy

`(1)/(2)mv^2=3.93623* 10^(-19)\\\Rightarrow v=\sqrt{(2* 3.93623* 10^(-19))/(9.5* 10^(-15))}\\\Rightarrow v=0.0091\ m/s`

The velocity of the bacterium would be 0.0091 m/s