Final answer:
The force exerted by the photons on a black surface when a laser beam of 0.5 J/s and 633 nm wavelength is totally absorbed is 1.67 nanoNewtons (nN).
Step-by-step explanation:
The force F exerted by the photons on a black surface when a laser beam is completely absorbed can be determined by calculating the momentum change Δp over the time Δt during which the momentum changes. We can use the power of the laser P and the wavelength of the light λ to find the force in nanoNewtons (nN).
First, we calculate the energy E of a single photon using the equation E = hc/λ, where h is Planck's constant and c is the speed of light. Then we find the number of photons N emitted per second by the laser using P = NE. Next, we use the fact that the momentum p of a photon is given by p = E/c, and the total momentum change per second Δp/Δt is equal to Np since the photons are entirely absorbed. As the force exerted by the photons is the rate of change of momentum, we get F = Np.
To apply the formula to the given laser beam with power 0.5 J/s (or 500 mW) and λ = 633 nm, we calculate the following:
- Energy per photon E = (6.63 x 10^-34 J-s)(3.00 x 10^8 m/s) / (633 x 10^-9 m) = 3.14 x 10^-19 J.
- Number of photons per second N = Power/Energy per photon = 0.5 J/s / 3.14 x 10^-19 J = 1.59 x 10^18 photons/s.
- Momentum per photon p = E/c = 3.14 x 10^-19 J / (3 x 10^8 m/s) = 1.05 x 10^-27 kg.m/s.
- Total force F = Np = (1.59 x 10^18 photons/s)(1.05 x 10^-27 kg.m/s) = 1.67 x 10^-9 N or 1.67 nN.