Question

The human eye can respond to as little as 10^−18 J of light energy. For a wavelength at the peak of visual sensitivity, 550 nm, how many photons lead to an observable flash?

Answer 1

3 photons

Step-by-step explanation:

The energy of a photon (E) can be calculated by the expression:

E = h*c/λ

Where h is the Planck constant (6.63x10⁻³⁴ J.s), λ is the wavelength (550 nm = 5.50x10⁻⁷m), and c is the speed of the light (3.00x10⁸ m/s).

E= (6.63x10⁻³⁴ * 3.00x10⁸)/(5.50x10⁻⁷)

E = 3.62x10⁻¹⁹ J

Which is the energy of one photon. The human eye can respond to 10⁻¹⁸ J, so:

1 photon ------------------------ 3.62x10⁻¹⁹ J

x ----------------------- 10⁻¹⁸ J,

By a simple direct three rule

x = 2.76 ≅ 3 photons.

Answer 2

The key equation is going to come from Mr Planck: E=h \\u

Where h is Plancks constant; and ν is the frequency. This equation gives you the energy per photon at a given frequency. Alas, you're given wavelength, but that's easy enough to convert to frequency given the following equation:

c= lambda / nu

where c is the speed of light; λ (lambda) is the wavelength; and ν is again frequency. As soon as you know the energy of a photon with a wavelength of 550nm, you should know how many photons you would require to accumulate 10^-18J. Be careful with your units.