What is the de Broglie wavelength for an electron that travels at #90%# the speed of light?

1 Answer
Aug 29, 2017

Answer:

See below

Explanation:

First we need to know the formula. It is, #λ = h/(mv)#
we know speed of light is #3.00 xx 10^8##m#/#s#, then we need to find what #90%# of that is.
To find that we do this,

#0.90c = 3.00 xx 10^8 "m/s" xx 0.90#

#=2.7 xx 10^8# #"m"//"s"#

#λ = h/(mv)#

#λ=# wavelength

#h=# Planck's constant, which is #6.63 xx 10^-34# #"m"^2 cdot ##"kg"//"s"#

#m=# mass of electron, which #9.11 xx 10^-31 "kg"#

#v=# velocity

#lambda =(6.63 xx 10^-34 "kg"cdot"m"^2//"s") / ((9.11xx10^-31 "kg") xx (2.7xx10^8 "m/s"))#

#=> lambda= 2.70 xx 10^-12"m"#