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Suppose a neutron of mass 1.67 X 10-27 'kg is traveling with the speed of 2200m What is the de Broglie wavelength of the neutron?...

Question

Suppose a neutron of mass 1.67 X 10-27 'kg is traveling with the speed of 2200m What is the de Broglie wavelength of the neutron?

Suppose a neutron of mass 1.67 X 10-27 'kg is traveling with the speed of 2200m What is the de Broglie wavelength of the neutron?



Answers

The de Broglie wavelength of a neutron is 0.01 nm. What is the speed and energy of this neutron?

So if we want to find the wavelength, we can use deplorables equation will plug in plank's constant on the top 6.626 times 10 to the negative 34th jewels, time seconds, and then on the bottom will plug in the mass, which is 1.67 times 10 to the negative 27 kg. You want kilograms because jules is expressed in terms of kilograms and then the velocity, which is 23 60 m per second, and you can evaluate this on your calculator, and you'll get 1.68 times 10 to the -10 in m.

Of the atom is essentially as considering the electron as a probabilistic matter waves. So the de Broglie wavelength is the wavelength related to the momentum of a particle, via the associated Plank's constant. And what this does is gives us the expression as follows. The wavelength is equal to Plank's constant, divided by the momentum. So the momentum is denoted P. While the momentum which is P is equal to m, see where we have mass and speed. So we can calculate P for the new trump, which is 1.6750 times 10 to the negative 24 g. And then we multiply that with the speed, which is 4.45 times 10 to the three m per second. We get a momentum of 7.605 times 10 to the negative 21 g per. Meet up a second. So we can substitute this value into the broadly equation. That was the first equation we looked at to find the wavelength where the wave length is equal to 6.626 times 10 to the negative 34 g per meters per second, divided by 7.605 times 10 to the negative 22 grounds for meet up at second, which is equal to 87.1 PK meters. So what we have is the following 87.1 PK meters, So the wavelength of a neutron traveling at 4.54 kilometers per second is 81 87.1 kilometers.

In this question, we are trying to find the wavelength off a neutron of Mass. 1.67 times, 10 to the minus 27 kilograms, traveling at a speed off 8.5 times, 10 to the full meters per second. So to answer this question and find the Waveland, I'm going to use the boys wavelength or do Brookly. However you want to pronounce the name, and that is that Lambda is equal to hate, which is Plank's constant, divided by momentum P. Let's remind ourselves that momentum P is equal to mass times velocity, for we can just input that in here and we got that hate over envy is equal toe Lunda. And that is why I'm using to Broich's wavelength, because mass and velocity is what we've been given in the question and hatreds a constant. So we have all the variables we need in this equation to calculate Lunda. So let's remind ourselves that Plank's constant is 6.63 times 10 to the minus 34. Now, you should either know that or have it written in your notes. That's not something a question. I usually give you the mass we're given is 1.67 times 10 to the minus 27. We don't need to change the units here as we've been given the mass in the S i units of kilograms on times not by the velocity, 8.5 turns tend to before. And if we put that into a calculator, we get that the wavelength comes out as 4.7 or 4.67 But I'm using two significant figures here times 10 to the minus 12 meters. Now, the convention with wave lands is that we usually give wavelengths in and nano meters. So I'm just gonna convert that answer to nano meters. So we know that nano meters ah times 10 to the minus nine. The prefix nano is times 10 to the minus nine. So if we're taking times 10 to minus nine, power away from this times 10 to the minus 12. We're left with times 10 to the minus three. And that is because if we have minus three minus nine, we get minus 12. So answer is 4.7 times 10 to the minus three nano meters, and that's just keeping with our unit convention. But this answer is also correct

To get a briefing for for a neutron. If a particle we have to use 80 broke restricting from not some dies goes to each overpay PC Moment. Um, so momentum is simply taking mass Times velocity, this case. All right, Since all of your CDs she last and the speed off liked by quite a bit. So you can use to, you know, relativistic momentum this case. Do you mess off to you, Neutron by 67 Sentinel Master. Seven kilograms, Bill C. They're struggling at 6.5 times. Temple full. It just sickened. And we should get about 6.1. It's 10 12 minutes, Jawf.


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