Textbook Exercise 1B.19

$\lambda=\frac{h}{p}$

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Textbook Exercise 1B.19

For this question should I be using the equation lambda=h/p and using the masses of a proton and neutron as well as the speed given? I am not sure how the percentage thing that is being asked works. I hope someone can provide some guidance. Thank you.

Question: Protons and neutrons have nearly the same mass. How different are their wavelengths? Calculate the wavelength of each particle when traveling at 2.75×105 m⋅s−1 in a particle accelerator and report the difference as a percentage of the wavelength of the neutron.

Anh Trinh 1J
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Re: Textbook Exercise 1B.19

Your equation is right for this question. I used $\lambda =\frac{h}{p}$ which is also $\lambda =\frac{h}{mv}$. Speed is given and the mass of a proton is $1.677\times 10^{-27} kg$ kg and neutron is $1.674\times 10^{-27} kg$.

The percentage it is asking for is how different are the wavelength of a proton and a neutron. Once you calculated the wavelength for both, you would find that the wavelength are identical to 3 significant figures.

Isaac Wen
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Re: Textbook Exercise 1B.19

To report the difference as a percentage of the wavelength of the neutron, use DeBroglie's λ=h/(mv) to first find the wavelength of the proton and neutron. Then, you want to subtract the wavelength of the neutron from the wavelength of the proton––and then divide that difference by the wavelength of the neutron. That being said, this question is just testing our conceptual understanding, so tbh the percentage calculation isn't super important!

905290504
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Re: Textbook Exercise 1B.19

just divide the difference of the wavelengths by the wavelength of the neutron and multiply that by 100% !