A laser emitting light of wavelength 660 nm has a power output of 18 W. It is used to irradiate a sample of a diatomic gas for 100 seconds. Assuming that each photon absorbed breaks exactly one chemical bond, how many moles of bonds are broken in the sample? (Take h = 6.6 10⁻³⁴ J s, c = 3 10^8 m s ⁻¹ , N_A = 6 10²³ mol ⁻¹ )

Step-by-step solution

Energy of one photon, E_p = hc E_p = 6.6 10⁻³⁴ 3 10^8 660 10⁻⁹ = 3 10⁻¹⁹ J Total energy delivered by the laser in 100 seconds: E_ total = Power time = 18 100 = 1800 J Total number of photons emitted: N = E_ total E_p = 1800 3 10⁻¹⁹ = 6 10²¹ photons Since each photon breaks exactly one bond, the number of bonds broken is 6 10²¹ . Number of moles of bonds broken = N N_A Moles = 6 10²¹ 6 10²³ = 0.01 mol Answer: 0.01