What is the momentum of a 4.00-centimetre-wavelength photon?
We can call the wavelength of this photon 𝜆. And we want to solve for its momentum, which we’ll call 𝑝. To begin, we can recall the relationship for the momentum of a photon. Photon momentum 𝑝 is equal to Planck’s constant ℎ over photon wavelength 𝜆.
Planck’s constant we’ll treat in this problem as exactly 6.626 times 10 to the negative 34th joule seconds. So 𝑝 equals ℎ over 𝜆. And when we plug in for these two values, being careful to use units of metres in our expression for 𝜆 and calculate 𝑝, we find that to three significant figures it’s 1.66 times 10 to the negative 32 kilograms metres per second. That’s the momentum this photon has.