Calculating Wavelength

[halle young 4A]

homework problem 1B.19

protons and neutrons have nearly the same mass. how much different are their wavelengths? calculate the wavelength of each particle when traveling at 2.75 x 10^5 m/s in a particle accelerator and report the difference as a percentage of the wavelength of the neutron.

can someone also please explain in depth the percentage part of the question?
thanks

[Mashkinadze_1D]

Remember that:
ƛ = h/p or ƛ = h/mv

For this solve first for the proton wavelength
ƛ = h/(1.6 x 10^-27kg)(2.75 x 10^5m/s)
ƛ = 1.4 x 10^-9

Solve for the neutron wavelength
ƛ = h/(1.76 x 10^-27 kg) (2.75 x 10^5m/s)
ƛ = 1.4 x 10^-12
Then:
(1.4x10^-9)/(1.4x10^-12) = 100%

If I did this correct than this would be representation as a percentage.

[AArmellini_1I]

So first you need to calculate the wavelength of both the proton and electrons with there respective mass. The formula you would use in this case would be: wavelength = h (planck's constant) / (mass x velocity). You kind find in the back of the book that the mass of a proton is (1.673 x 10^-27)kg and for an electron it is (1.675 x 10^-27)kg. Plugging in the corresponding values you find the wavelength of both protons and electrons to be approximately 1.44pm. Therefore there wavelength are identical to 3 sig figs

[EvaLi_3J]

Hi!
I haven't done this problem before but I think what it means is that after you calculate the difference of the wavelengths (between protons and neutrons), you need to then calculate how much of the wavelength of neutron does this difference in wavelengths take up. Namely, diff divide by wavelength of neutron.

Just my assumption, if anyone has a better understanding, please correct me.

[Jialun Chen 4F]

I got the same conclusion/answer as AArmellini did. There is no difference when I used 3 sig.figs in that problem.

[Sean Cheah 1E]

Hi!
I haven't done this problem before but I think what it means is that after you calculate the difference of the wavelengths (between protons and neutrons), you need to then calculate how much of the wavelength of neutron does this difference in wavelengths take up. Namely, diff divide by wavelength of neutron.

Just my assumption, if anyone has a better understanding, please correct me.

I believe that this is the correct approach. The problem specifically asks for the difference as a percentage of the wavelength of the neutron. Therefore, once you calculate the two wavelengths using the masses from the back of the book, the given velocity, and DeBroglie's equation, find their difference, divide that by the wavelength of the neutron, and multiply the result by 100% to get your final answer.