Question

the human eye is a complex sensing device for visible light. the optic nerve needs a minimum of 2.0 multiplied by 15J of energy to trigger a series of impulses that eventually reach the brain. how many photons of red light (682nm) are needed?

I think I got the answer...just want to make sure I did it right. If you could show the steps and the answer, that would be great.

Also, I know the question is written weird. My instructor said that “2.0 multiplied by 15J” is the same as 30J

Answer 1

Step 1: Explanation

A photon is the smallest unit of electromagnetic radiation. So, it is the basic unit of all light. Photon is an imaginary concept. It is a charge less and mass less particle which is always in a state of motion.

For a photon of wavelength λ meters.

Energy of one photon = hc / λ   where h = planck's constant = 6.626 × 10^-34 J-s and C = 3 × 10⁸ m/s =speed of light

Hence for energy of N photon just multiply by N

Energy of N photon = N × ( hc / λ )

Step 2: Calculation

Energy= 2×15 J = 30 J [ assuming that the data is correct ]

λ = 682 nm = 682 × 10^-9 m [ because 1nm = 10^-9 m ]

By using the above equation

Energy of N photon = N × ( hc / λ )

=> N = Energy /  ( hc / λ )

=> N = ( Energy × λ ) / hc

By putting their values, For red light photons, we get

=> N = ( 30 J × 682 × 10^-9 m ) / ( 6.626 × 10^-34 J-s × 3 × 10⁸ m/s ) = 1.03  × 10²⁰ photons of red light

So, 1.03  × 10²⁰ of red light photons are needed.