photons

Question

Hypothetically if the 40W bulb only produced green light, and 10% of the energy consumed was used to produce green light (λ=500nm), the number of photons produced each second is ___x10¹⁹ 

Answer 1

Wave length of the bulb is λ=500 nm = 500 × 10^-9 m

The Energy of one photon can be found using the formula E_p = h*f .

Where h is plank's constant = 6.63 × 10^-34 J·sec .

            f is the frequency of light . 

The frequency of the can be found using the formula f = c/λ .

Where c = velocity of light = 3 × 10⁸ m/s .

E_p = (h*c)/λ 

E_p = (6.63 × 10^-34  × 3 × 10⁸ )/ 500 × 10^-9

E_p = 3.975 × 10^-19  J .

40 w of bulb means  = 40 Joules /sec .                                    (Since 1 watt = 1 Joule / sec ) 

We know that total energy E = N * E_{p .}

Where N is number of photons .

Out of 40 joules of energy , only 10% of energy was used to produce light (E) ⇒ 40 *(10/100)  = 4 J

N = E / E_p 

Number of photons N =  4 J / 3.975 × 10^-19  J

N = 1.006126 × 10¹⁹  Photons per second .

Hence the number of Photons produced each second is 1.006126 × 10^{19 .}