A light bulb with a power rating of 100 W converts 20 % of its electrical energy into monochromatic light of wavelength 400 nm . The number of moles of photons emitted by the bulb in 10 minutes is x 10⁻³ . The value of x is _____. (Nearest integer) (Given: h = 6.626 10⁻³⁴ J s , c = 3 10^8 m s ⁻¹ , N_A = 6.022 10²³ mol ⁻¹ )

Step-by-step solution

Useful power of the light bulb (energy emitted as light per second): P_ useful = 100 W 20 100 = 20 W = 20 J s ⁻¹ Total energy emitted as light in 10 minutes : E_ total = P_ useful t = 20 (10 60) = 12000 J Energy of one mole of photons of wavelength 400 nm : E_ mole = N_A hc E_ mole = 6.022 10²³ 6.626 10⁻³⁴ 3 10^8 400 10⁻⁹ E_ mole = 119.71 10⁻³ 400 10⁻⁹ = 299275 J mol ⁻¹ Number of moles of photons emitted: n = E_ total E_ mole n = 12000 299275 0.0401 moles n = 40.1 10⁻³ moles Comparing this with x 10⁻³ , we get x 40