Question

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.

Answer 1

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 9.10938356×10^-31 kg. So p = mv p/m = v 3.31303502x10^-27 kg*m/s / 9.10938356×10^-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.