Question

The human eye is a complex sensing device. The optic nerve needs a minimum of 2.10x10^-17J of energy to trigger a series of impulses that eventually reach the brain. How many photons of blue light (475nm) are needed? The human eye is a complex sensing device. The optic nerve needs a minimum of 2.10x10^-17J of energy to trigger a series of impulses that eventually reach the brain. How many photons of blue light (475nm) are needed? @Chemistry

Answer 1

there are 2 equations that link wavelength of light and the energy that a single photon of that wave of light carries. One is \[c = \lambda * \nu\] where C is the speed of light (3*10^8m/s). The other is \[E = h * \nu\] where h is Plank's constant (6.626*10^(-34)J*s). The "nu" is the frequency of the wave of light. These 2 will allow you to calculate the energy of a single photon of light, so long as you know its wavelength.\[\nu = \frac{c}{\lambda} = \frac{3.0*10{^8}\frac{m}{s}}{475*10^{-9}m} = 6.32*10^{-14}s^{-1}\]
Plug that frequency into the second equation\[E = h*\nu = (6.626*10^{-34}J*s) *(6.32*10^{-14}s^{-1}) = 4.18*10^{-19}J\]so a single photon of blue light possesses that much energy. In order to trigger a response from the eye, you need\[2.17*10^{-17}J * (\frac{1photon}{4.184*10^{-19}J}) = 51.8 \approx 52 photons\]