Exercise 1B 19

[Brian Chhoy 4I]

The question states that "protons and neutrons have nearly the same mass. How different are their wavelengths? Calculate the wavelength of each particle when traveling at 2.75 * 10^5 m/s in a particle accelerator and report the difference as a percentage of the wavelength of the neutron."

I tried solving it by using the mass of each particle, proton and neutron, and plugging it into the equation for kinetic energy: 1/2 m v^2, with v being the velocity traveling in the particle accelerator. I then plugged in the energy calculated into the manipulated formula for wavelength, (hc)/E. With that I got 3.138 nm for the neutron and 3.143 for the proton. I subtracted the mass of the neutron from the mass of the proton and then divided that by the mass of the neutron, which I then multiplied by 100 to get the percentage of a neutron, the proton is longer by. Is this correct, I wasn't sure if I could solve for the wavelength using these equations. Thanks.

[Camille Marangi 2E]

The way I answered this problem was to use the equation λ=h/mv. So we have Planck's constant as h=6.626x10^-34 J.s, velocity is given as 2.75x10^5 m/s and then you would do this equation twice, once using the mass of the proton (m=1.673x10-27 kg) and again using the mass of the neutron (m=1.674x10^-27 kg). These masses are almost identical which is what the problem wants to point out, I think.So after using those equations the wavelength comes out to 1.439x10-12 m for the neutron and 1.440x10-12m for the proton. With sig figs taken into account the wavelengths are exactly the same, 144 pm.

Hope this helped!

[Chloe Orsini 1K]

A lot of people seem to also be struggling between using the debroglie equation and kinetic energy. The equation you attempted to use does not allow us to solve for wavelength. The de broglie equation λ = h/mv, uses plancks constant, mass, and velocity to solve for wavelength.