In order to "see" something smaller than about 200 nm, an electron microscope can be used. an electron would have to be traveling at ___________ m/s in order to have a de broglie wavelength of 200 nm.
3640 m/s
The de Broglie wavelength of a particle is expressed by the equation:
λ = h/p
where
λ = wavelength
h = Planck constant
p = momentum
so let's solve for momentum and the substitute the known values and calculate:
λ = h/p
λp = h
p = h/λ
p = 6.62607004x10^-34 Js/2x10^-7 m
p = 6.62607004x10^-34 kg*m^2/s^2 * s/2x10^-7 m
p =3.31303502x10^-27 kg*m/s
Now momentum is defined as mass times velocity. And the mass of an electron is 9.10938356Ă—10^-31 kg. So
p = mv
p/m = v
3.31303502x10^-27 kg*m/s / 9.10938356Ă—10^-31 kg = v
3.63694754774384x10^3 m/s = v
Rounding to 3 significant figures gives 3.64x10^3 m/s or 3640 m/s. That velocity is low enough that we don't need to worry about relativistic effects.
