A photon has momentum of magnitude 8.24 * 10-28 kg # m>s. (b) What is the wavelength of this photon? In what region of the electromagnetic spectrum does it lie?

Video transcript

Hi, everyone. In this practice problem, we will consider a photon and the light emitted by a laser device that has a momentum of 7.23 times 10 to the power of 28 kg meters per second. We're being asked to determine in which part of the electromagnetic spectrum this photon's wavelength lies. And the options given are a infrared B visible C radio and D ultraviolet. So uh basically what this question is asking is the wavelength of the photon. So let's start by calculating that. So we want to recall that the momentum of a photon is going to be represented by B which is equals to H divided by lambda. H is going to be the plan's constant, which is going to be 6.6, 26 times 10 to the power of negative 34 seconds. And LAMBDA is just going to be our wavelength of our photons. So lambda, we wanna, what we're interested to find is our lambda here because the momentum and the uh plants constant is known, the plant's constant is constant and the momentum is given in the problem statement. So we want to arrange our equation. So that we get an equation for lambda, which is just going to be H divided by B. So substituting our values in we have H two B 6.6 to times 10 to the power of negative 34 2 seconds divide that by our momentum of the photon which is 7.23 times 10 to the power of 28 kg meter per second. And then that will actually give us our wavelength or LAMBDA which will actually come up to a value of 9.16 times 10 to the power of negative seven m. We wanna convert that into nanometer for uh just so that it's easier for us to determine what spectrum it actually lies into. So we want to multiply this with 10 to the power of nine nanometer for every one m and they'll give us a lambda value of 916 nanometer. The wavelength of 916 nanometer is going to be longer than visible light and actually lies in the infrared spectrum. So the answer to this practice problem is going to be infrared which will correspond to option A. So the part at which the electromagnetic spectrum or at which this photons wave flang lice is going to be the infrared spectrum, which is going to correspond to option A. So that'll be it for this video. If you guys still have any sort of confusion, please make sure to check out our adolescent videos on similar topics but other than that, they'll be it for this one. Thank you.