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Problem 38 Easy Difficulty

A high-energy particle scattered from the nucleus of an atom helps determine the size and shape of the nucleus. For best results, the de Broglie wavelength of the particle should be the same size as the nucleus (approximately $10^{-14} \mathrm{m} )$ or smaller. If the mass of the particle is $6.6 \times 10^{-27} \mathrm{kg},$ at what speed must it travel to produce a wavelength of $10^{-14} \mathrm{m} ?$

Answer

$1.004 \times 10^{7} \mathrm{m} / \mathrm{s}$

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Top Physics 103 Educators
Christina K.

Rutgers, The State University of New Jersey

Marshall S.

University of Washington

Zachary M.

Hope College

Meghan M.

McMaster University

Video Transcript

our question wants us to consider a particle whose wavelength Lambda is 10 to the minus 14 meters and mass M a 6.6 times 10 to the minus 27 kilograms. Its assets is to find the velocity of this particle to create this wavelength. So we're gonna use the dobro J wavelength, which gives us the wavelength of a particle relative to its momentum. So lambda here is equal to Planck's constant H divided by the mo mentum P momentum momentum classically is mass times velocity. So this is place constant H divided by mass times velocity. So we simply rearrange this equation to sulphur velocity. We find it's equal to Planck's constant divided by the mass times the wavelength. We're given the mass in the wavelength. In the beginning of the question and planks, costume is equal to 6.625 times 10 to the minus 34 jewell seconds. So plugging these values in, we find that this is equal to 1.4 times 10 to the seven meters per second. We can go ahead and box this and is the solution to our question

University of Kansas
Top Physics 103 Educators
Christina K.

Rutgers, The State University of New Jersey

Marshall S.

University of Washington

Zachary M.

Hope College

Meghan M.

McMaster University