Electrons moving in a beam have the same de Broglie wavelength as protons moving in a separate beam. The proton beam moves at a speed of 3.1 x 10^4 m/s. What is the speed of the electrons?

From the data sheet, the de Broglie wavelength, ๐œ† = h/p = h/(mv)
The electron wavelength equals the proton wavelength so: ๐œ†e = ๐œ†p
So: h/(meve) = h/(mpvp)
meve = mpvp
so the electron speed, ve = (mpvp)/me
From the data sheet, the rest mass of an electron and a proton respectively are: me = 9.11x10-31kg, and: mp = 1.67x10-27kg
Subbing these values along with the proton speed from the question gives:
ve = (1.67x10-27 x 3.1x104)/( 9.11x10-31)
ve = 5.7x107ms-1

Answered by Alexandra G. โ€ข Physics tutor

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