Answer:
Minimum number of photons required is 1.35 x 10⁵
Explanation:
Given:
Wavelength of the light, λ = 850 nm = 850 x 10⁻⁹ m
Energy of one photon is given by the relation :
[tex]E=\frac{hc}{\lambda}[/tex] ....(1)
Here h is Planck's constant and c is speed of light.
Let N be the minimum number of photons needed for triggering receptor.
Minimum energy required for triggering receptor, E₁ = 3.15 x 10⁻¹⁴ J
According to the problem, energy of N number of photons is equal to the energy required for triggering, that is,
E₁ = N x E
Put equation (1) in the above equation.
[tex]E_{1}=N\times\frac{hc}{\lambda}[/tex]
Substitute 3.15 x 10⁻¹⁴ J for E₁, 850 x 10⁻⁹ m for λ, 6.6 x 10⁻³⁴ J s for h and 3 x 10⁸ m/s for c in the above equation.
[tex]3.15\times10^{-14} =N\times\frac{6.6\times10^{-34}\times3\times10^{8}}{850\times10^{-9}}[/tex]
N = 1.35 x 10⁵
