Question

(6pts) Can You See a Single Photon? The wavelength corresponding to the maximum sensitivity

of the human eye is 510 nm, the limit of sensitivity of the dark-adapted eye has been shown to be correspond to

a 100 ms flash of light of total energy 240 eV. (Little Shop of Physics- Colorado State University)

1 J = 6.241509 x 10¹⁸ eV

a) What is the energy of a single photon at this wavelength?

b) How many photons does the flash contain?

c) If 60% of the incident light is lost to reflection and absorption by tissues of the eye, determine how many photons reach the retina and if you can see a single photon?

Answer 1

a) Wavelength = 510nm = 510×10^-9m

wavelength = speed of light / frequency

frequency = speed of light / wavelength

= 2.99×10^8(m/s)/510 ×10^-9m

= 5.86×10^14s^-1

Energy = hv

h = planck constant , 6.626×10^-34J.s

v = frequency

Therefore,

E = 6.626×10^-34J.s × 5.86×10^14s^-1

= 3.88×10^-19J

b) Energy of flash = 240eV

1eV= 1.602×10^-19J

240eV = 240×1.602×10^-19J = 3.84×10^-17J

No of poton = 3.84×10^-17J/3.88×10^-19J

= 99photons

c) (60/100) × 99photons = 59photons

Therefore,

not possible to see single photon