Practice Problem 1B.19

[Diego Salgues 2K]

In the textbook, I have trouble with the problem 1B.19.

"Protons and neutrons have nearly the same mass. How different are the wavelengths? Calculate the wavelength of each particle when traveling at 2.75 x 10^5 m/s in a particle accelerator. Find the difference as a percentage of the wavelength of the neutron".

I am not sure on how to calculate something as a percentage of the wavelength of the neutron. How do I do this?

Thank you,

D

[emmakvarnell]

Hi!

First you should use the equation wavelength=h/p=h/(mV), because p=mV to find the wavelength of the electron at that speed, and then find the wavelength of the proton at that speed. Both of these masses can be found on the equation sheet. To get the percentage, use the equation sheet to find the mass of the neutron, and calculate the wavelength of the neutron at the given speed. Then divide the electron's wavelength by the neutron's wavelength and multiple by 100%, and do the same for the proton and neutron. From here you can compare the resulting percentages.

[Sophia Zhao]

Percentage is the ratio of two things expressed out of 100. Dividing the proton's wavelength by the neutron's wavelength gives you the ratio of the two (or percentage) in terms of the neutron's original wavelength. Percentage is calculated as x/y * 100%. Whenever a problem asks for the percentage of something in terms of _____, ______ should be the denominator in the fraction (or y).