HW 1.37 [ENDORSED]

[Kaleb Tesfaye 1I]

Protons and neutrons have nearly the same mass. How different are their wavelength? Calculate the wavelength of each particle when traveling at 2.75*10^5 m s^-1 in a particle accelerator and report the difference as a percentage of the wavelength of the neutron.

In order to calculate their wavelengths, we need to use DeBroglie's equation but i don't understand how we are supposed to calculate the percentage of the wavelength of the neutron. Do we simply divide the wavelength of the neutron by the wavelength of the proton and then multiply by 100 to get the percentage?

[Jack Martinyan 1L]

After finding the values of both the wavelengths for the proton and the neutron, subtract the wavelength of the neutron from the wavelength of the proton. After you find the difference, multiply the difference by 100 and divide it by the wavelength of the neutron to find out what percentage of the neutron's wavelength the difference comprises. Since the mass of protons and neutrons is so similar, you would have to use a good amount of decimal places to actually find a percent difference.

[Sophia Diaz - Dis 1B]

Just to make sure I did the problem correctly, I got the same number for both of the parts. Did I use too little sig figs (I used 3) or is this the same thing that you guys got? And if they are the same number does that mean that there's 0% difference between them? Thanks!

[Chem_Mod]

You may need to use more digits if you want to see a difference.

[victoriatanaka1C]

Would the answer be "the wavelength of a proton is x% larger than the wavelength of a neutron"?

[Rosamari Orduna 1D]

the answer given by the book is 1.44pm, but if we want a difference in percentage, which is a second thing they are asking for, do we use exact numbers to get that? Or should we not worry about it since, the answer key states they are "identical"?
I got a 0.01% difference but I used 6 sigfigs, i believe..

Is most of this just relevant to the sig figs we use?

[AnthonyDis1A]

Being more precise and using more decimal places got me a percent difference closer to 0, but it's probably negligible since proton and neutron masses are already pretty close in value.