What is the momentum of a gamma-ray photon with a wavelength of 4.00 times 10 to the negative 13 meters? Use a value of 6.63 times 10 to the negative 34 joule-seconds for the Planck constant. Give your answer in scientific notation to two decimal places.
Remember, photons have no mass. So, their momentum is actually defined by the equation 𝑃 equals ℎ divided by 𝜆, where 𝑃 is the momentum of the photon, ℎ is the Planck constant, and 𝜆 is the photon’s wavelength. We are given a value for the photon’s wavelength and also a value for the Planck constant. So, to find the momentum, all we need to do is substitute values into this formula. We have 6.63 times 10 to the negative 34 joule-seconds divided by 4.00 times 10 to the negative 13 meters. The numerical portion of this result is exactly 1.6575 times 10 to the negative 21. The units are joule-seconds divided by meters. And we know that the final units must agree with momentum.
Expressed in terms of SI base units, momentum has units of kilogram-meters per second. Since joules can be expressed directly in terms of SI base units, joule-seconds divided by meters will give us the SI base units for momentum, kilogram-meters per second. So, the momentum of our photon is 1.6575 times 10 to the negative 21 kilogram-meters per second, which rounding to two decimal places is 1.66 times 10 to the negative 21 kilogram-meters per second.