Question

The wavelength of a nonrelativistic electron is 1.900e-6 m. How fast is it moving? Express your answer as a fraction of the speed of light, c.

Answer 1

Given Data

wave length = ? = 1.90 * 10^-6 m

We have

h is plank constant, 6.62 x 10^-34
m is mass of electron, 9.11 x 10^-31 kg

speed, v = ?

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from the debrogile wave length of matter waves : Lambda = h/mv
                                                                        v = h/Lambda*m
                                                                        = (6.62 * 10^-34 J.s) / (1.900 * 10^-6 * 9.11 *10^-31 kg)
                                                                      v = 382.46 m/s

In terms of fraction of the speed of light is v = 382.46 m/s / (3*10^8)

                                                                  = 1.27*10^-6 c --> Answer

(or)

Wavelength of electron is ? =1.90*10^-6 m

          speed of theelectron is v = 1 / ? * c
                                                   = 1 / 1.90*10^-6 m * c
                                                   = 0.526*10⁶ c