## Textbook Problem- 1B.19

$\Delta p \Delta x\geq \frac{h}{4\pi }$

CNourian2H
Posts: 106
Joined: Fri Aug 30, 2019 12:16 am

### Textbook Problem- 1B.19

Hi guys, I'm confused with this textbook problem. Can anyone describe the steps needed to complete the problem?

1B.19 Protons and neutrons have nearly the same mass. How different are their wavelengths? Calculate the wavelength of each particle when traveling at 2.75 x 10^5 mxs^-1 in a particle accelerator and report the difference as a percentage of the wavelength of the neutron.

Tracy Tolentino_2E
Posts: 140
Joined: Sat Sep 07, 2019 12:17 am

### Re: Textbook Problem- 1B.19

We would use De Broglie's equation wavelength=Planck's constant/(mass of particle x velocity).
Planck's constant: 6.626 * 10^-34 J.s
mass of proton: 1.673 * 10^-27 kg
mass of neutron: 1.675 * 10^-27 kg
velocity: 2.75 * 10^5 m/s

wavelength of proton = 6.626 * 10^-34 J.s / ((1.673 * 10^-27 kg) * (2.75 * 10^5 m/s))
=1.44 * 10^-12 m or 1.44 pm

wavelength of neutron = 6.626 * 10^-34 J.s / ((1.675 * 10^-27 kg) * (2.75 * 10^5 m/s))
=1.44 * 10^-12 m or 1.44 pm
The wavelengths of a proton and neutron are the same.