what-speed-must-a-neutron-have-if-its-de-broglie-wavelength-is-to-be-equal-to-the-interionic-spacing

Question

What speed must a neutron have if its de Broglie wavelength is to
be equal to the interionic spacing of table salt $(0.282 \mathrm{nm})$ ?

Zulfiqar Ali · Accepted Answer

well enter I own expressing off table salt ical zero point to it Multiply. Return to the power minus nine meters. Uh inter ionic. Enter ionic passing is equal. Do zero point 282 multiply by 10 to the power minus nine meters. Months off. Neutron must off. Neutron is equal to 1.674 multiplied by tend to the bar minus 27 kilograms. Well, we know that the probably that length is called toe playing constantly writing momentum solving. For Ricky, the lost T is equal toe, each divided by mass times. Ah, back Clint. Let&#x27;s plug in the values, which is 6.63 Multiply by 10 to the power minus 34. Jule second, divided by must off neutron is 1.674 Multiply by 10 to the power minus 27 kilogram times. The battle in and prevalent equals zoo point ah 0.28 to multiply Returned to the power minus mine meters way is equal to ah six point 63 multiplied by 10 to the power minus 34 divided by ah zero point for uh, seven multiplied by 10 to the dollar minus 36 dividing the two numbers, velocity is equal to 14 0.4 multiplier. I turned to the power to and this can be further returning. Sze one point for multiply by 10 to the power tree meter per second since 10 to the power tree is a killer, therefore lost years ago in tow, one point for kilometer for a second.

Bret Rosen · Answer

in this problem were given a neutron with age Burghley wavelength of 0.1 nanometers and were asked to calculate the velocity and energy of the neutron. Uh, eso What we use for this problem is Thebe broccoli relationship for wavelength and momentum. So lambda equals h overpay, which is describing are particles when they&#x27;re in transit as waves. And then so just looking at this, it looks, uh, like the like a non relativistic speed so we can check that at the end. But we&#x27;ll use some Newtonian equations to go from mo mentum p to kinetic energy and then from kinetic energy to velocity. And so we&#x27;ll solve those Newtonian equations for kinetic energy and velocity, and then we&#x27;ll check to make sure that our assumption that it is a non relativistic speed is correct. Okay, some constants that will need Here are plank constant H 6.626 times 10 to the minus 34 Jewell. Second, our mass of our neutron is 1.674 93 times 10 to the minus 27 kilograms and the wavelength of our neutron that were given here 0.1 Animators and in meters, it will be 10 to the minus 11 m. All right, so are the broccoli equation. Lambda equals h overpay. And again, who are assuming this is non relativistic. So we can say p equal to to screw it mass times kinetic energy. And so we&#x27;re going to solve s We&#x27;ll solve that for kinetic energy. So we get to m kay right equal to H Squared over Lambda Squared. And so now we&#x27;ve got our kinetic energy equal to H Squared over to em Lambda squared. And so that&#x27;s going to give us. I will have our our denominators. We&#x27;ve got to 1.67493 10 to the minus 27 kg and can on a 11 m squared. So the denominator and our numerator 6.626 10 to the minus 34 Jules, second squared. And so if we work that out, we get our kinetic energy equal to 1.3106 times 10 to the minus 18. Jules. Okay. And now we&#x27;ll go from kinetic energy, uh, to velocity. So okay equals to one half mv squared, and we&#x27;ll solve that for velocity. So we get V equals to square it two k over em and that is going to be too. One point 3106 10 to the minus 18 jewels and right by our mass went 67493 10 to the minus 27th kilograms. And that works out to be 39,000 559.6 meters per second. Okay. And to take this thio three significant figures here, so are, um energy is equal to 1.31 standard the minus 18 jewels and our velocity equal thio 3.96 times 10 to the fourth meters per second. So those are the quantities we were looking for And so let&#x27;s just check that are were in a non relativistic situation so that three terms tend to the it&#x27;s about four times 10 to the fourth is about 0.1 tons thes speed of light. And so that is Ah, speed, weaken say is non relativistic. And so our assumption waas good

Zachary Warner · Answer

we&#x27;re told that we have a particle of mass him in a dip Roj wavelength of Lambda were asked to find the speed at which this particle must be moving. The goal. J wavelengths says that Lambda is equal to Planck&#x27;s constant H, divided by mass times velocity. Therefore, we just rearrange this to find the velocity or speed, and we find that it&#x27;s equal to H over him times lambda Plugging these values into this expression, we find that too, you velocity value for the speed is equal to 1.41 Tanks tend to the third meters per second Megan box. That is the solution to our question.

Vipender Yadav · Answer

So here in this problem were given that the distance between atoms off any seal crystal iss 0.2 it in nanometer. And where to calculate that at what speed the neutron must be moving so that the deep Roy wavelength is 0.28 nanometer. We know that the expression for Deb Roy Equivalent Linda is given by H Overpay, where h is Planck&#x27;s constant on DPI is a moment momentum, so they can, you know momentum. Is the product off mass on the velocity. So in pocket here edges equals toe m times we. So from here, we&#x27;ll get the expression off The last two years each over M Linda, we had to calculate the velocity. You obtained the expression you can plug all the village here so we lost. It will be called Toe Plank&#x27;s constant. Its value is 6.6 26 times 10 to the power minus 34. Jewell sickened divide by moss off neutron. We know it&#x27;s 1.68 times turned to the power minus 27 k g multiplied by Lambda. We have 0.28 nanometer, but we have to convert this thing into meter So for that will be multiplying it with 10 to the power minus nine. So this much off the meter now can simplify this on. We&#x27;ll get the answer as 14.9 times 10 to the power to meet a per second. So this is required. Velocity off neutral toe. Get the d Brive Evelyn as 0.2 it nanometer. So I hope you have understood the problem. Thank you.

Zulfiqar Ali · Answer

don&#x27;t even have lent off. Neutrons is equal to 0.250 nanometers. All right, so, de promptly. Fab lint. He promptly, you fab lint The broadly babble int um off neutrons off named drones. It&#x27;s equal to 0.25 Sydell nanometers and 0.250 nana meters. It&#x27;s equal to 0.250 multiplied by 10 to the power minus mind maters and enter eye on expensive crystal eyes equal to inter. Alan expressing, uh is D uh, Andy is equal to zero point 0.282 nanometers in meters. We have zero point toe 82 multiply by 10 to the power minus nine meters part, eh? Let&#x27;s find out. Speed off neutrons. We know they&#x27;d momentum equals etch divided by lander. And this can&#x27;t be returnees. M we, uh, most times we lost you, which is momentum is equal to each divided by Linda. And from this ingredient, velocity equals velocity Physical too edge divided by mass times that link. Let&#x27;s plug in the values. Uh, velocity is equal to ah 6.63 Multiply by 10 to the power minus 34. Jule second divided by Moss. A month&#x27;s off neutron ISS 1.674 multiply by 10 to the power minus 27 kilograms. Multiply by, um prevalent and valent is equal to zero point 250 multiplied by 10 to the power minus nine minus nine Dividing, uh, these numbers dividing plan constant by lambda Um, we get, uh, momentum and from momentum equation, we can find out. Speed and speed is a call to, um 15 0.84 Multiply by 10 to the power to and this gives us 1584 meter per 2nd 1584 meter for a second part B. Well, we know it to be. Scientific data is equal to m times later. Lambda. Sorry, Andi. Is the inter around expressing on dhe scientist A equals R M times Linda divided by two times D here em is a cold too. And therefore signed Tita is equal to, um to multiply by, um lander, which is 0.2 50 multiplied by 10 to the power minus nine. Divided by to multiply by D is 0.282 Multiply returned to the bar minus nine and scientist er is equal to zero point and it&#x27;s six and Tito equals Sinan worse off zero point it six and signing worse of 0.86 is a cool too 62.4 three decrees.

Jheremiah Simon · Answer

let&#x27;s consider a case where we have a proton with a wavelength of two nanometers and we want to find the velocity of that proton so we can use our typical equation, which is the wavelength. Lambda is equal to plank&#x27;s constant, divided by mass times volume solving for velocity we will get velocity is equal to plank&#x27;s constant over the mass times the wavelength. So our wavelength in this case is two nanometers. So let&#x27;s convert that over two meters. So to convert that two meters, you would do two times one times 10 to the negative nine, which is just going to give you two times 10 to the negative nine. So that is it in meters now. So we have a chew over here in the top left. Our lambda is now right here and then the mass of a proton is over here on the left. So not that one. The two with the green dots next to them are the two you&#x27;re gonna need and the one with the green line under it. You plug all of that into your equation. No, not land. And we get velocity equals 100 and 98 meters per second.

Problem

A 71 -kg jogger runs with a speed of 4.2 $\mathrm…

Problem 63 Medium Difficulty

What speed must a neutron have if its de Broglie wavelength is to
be equal to the interionic spacing of table salt $(0.282 \mathrm{nm})$ ?

Answer

$1.4 \times 10^{2} \mathrm{km} / \mathrm{s}$

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$1.4 \times 10^{2} \mathrm{km} / \mathrm{s}$

Physics

Elyse G.

Christina K.

Andy C.

Jared E.

Wave Optics - Intro

Multiple Aperture Interference - Overview

James S. WalkerPhysics

Elyse G.

Christina K.

Andy C.

Jared E.

James S. Walker

Physics