Question

Suppose 10−17J of light energy is needed by the interior of human eye to see an object .The photons of green light (λ=550nm) needed to see the object are :

Answer 1

amount of energy is required by the interior of human eye to see an object , E = 10^-17 J

we have to find number of photons of green light needed to see the object.

wavelength of green light , λ = 550 nm = 5.50 × 10^-7 m

so, energy of one photon, e = hc/λ

= (6.63 × 10^-34 × 3 × 10^8)/(5.5 × 10^-7)

= (19.89 × 10^-26)/(5.5 × 10^-7)

= 3.616 × 10^-19 J

Let number of photons = n

then, energy of n photons, E = ne

= n × 3.616 × 10^-19 J

now, 10^-17 J = n × 3.616 × 10^-19 J

or, 10² = n × 3.616

or, n = 100/3.616 = 27.65 ≈ 28

hence, number of photons of green light needed to see the object are 28.

Answer 2

wavelength of green light , λ = 550 nm = 5.50 × 10^-7 m

so, energy of one photon, e = hc/λ

= (6.63 × 10^-34 × 3 × 10^8)/(5.5 × 10^-7)

= (19.89 × 10^-26)/(5.5 × 10^-7) = 3.616 × 10^-19 J

Let number of photons = n

then, energy of n photons, E = ne

= n × 3.616 × 10^-19 J

now, 10^-17 J = n × 3.616 × 10^-19 J

or, 10² = n × 3.616

or, n = 100/3.616 = 27.65 ≈ 28 hence, number of photons of green light needed to see the object are 28.