Question

6) Calculate the wavelength of an electron, in pm, when its velocity is 2.9978 x 106 m/s.

Answer 1

Ans. The wavelength of an electron travelling with certain velocity is given by-

            l = (h / p)        - equation 1

            Where, l = de Broglie wavelength of an electron (or other particle)

                        h = Plank’s constant = 6.626 x 10^-34 Js = 6.626 x 10^-34 m² kg s^-1

                        p = momentum of the particle = mv = (mass x velocity) of the particle

Given, v = 2.9978 x 10⁶ ms^-1

Mass of electron, m = 9.109 x 10^-31 kg

Putting the values in equation 1-

            l = (6.626 x 10^-34 m² kg s^-1 ) / [(9.109 x 10^-31 kg) x (2.9978 x 10⁶ ms^-1)]

            Or, l = (6.626 x 10^-34 m² kg s^-1 ) / (27.3069602 x 10^-25 kg m s^-1 )

            Or, l = 2.43 x 10^-10 m

Hence, wavelength of the electron = 2.43 x 10^-10 m