A beam of red laser light (λ = 633 nm) hits a black wall and is fully absorbed. If this exerts a total force F = 5.9 nN on the wall, how many photons per second are hitting the wall?
To calculate the number of photons per second hitting the wall, we can use the formula:
Number of photons = Power / Energy per photon
First, let's find the power of the laser beam using the given force.
Power can be calculated using the formula:
Power = Force * Velocity
Here, we know the force (F = 5.9 nN) but not the velocity. However, we can relate force to momentum using the equation:
Force = Rate of change of momentum
Since momentum (p) is defined as the product of mass (m) and velocity (v):
Force = m * Δv / Δt
For photons, the mass is negligible, so the force can be expressed as:
Force = Δp / Δt
where Δp is the change in momentum over a certain time interval Δt.
Since light is absorbed by the wall, the momentum change experienced by the wall is equal to the change in momentum per photon hitting the wall. Therefore:
Force = Δp / Δt = Δp / (1/f) = f * Δp
Here, f is the frequency of the photon.
The energy (E) of a photon can be given by the equation:
E = hf
where h is Planck's constant.
We know the wavelength of the laser light (λ = 633 nm) and want to find the energy per photon, so we can use the equation:
c = λf
where c is the speed of light.
Rearranging the equation, we get:
f = c / λ
Substituting this expression for frequency into our force equation:
F = f * Δp
Simplifying, we get:
Δp = F / f
Δp = F / (c / λ)
Δp = F * λ / c
Now we have the change in momentum per photon. We need to calculate the energy per photon using the equation E = hf = hc / λ.
Therefore:
Energy per photon = hc / λ
Finally, substituting the given force, wavelength, and speed of light into the formulas, we can find the number of photons hitting the wall per second.