33) An electron has a de Broglie wavelength of 0.18 nm. a) How large a potential

Question

33) An electron has a de Broglie wavelength of 0.18 nm.

a) How large a potential difference did it experience if it started from rest ?

b) If a proton has a de Broglie wavelength of 0.18 nm, how large is the potential difference it experienced if it started from rest ?

Explanation / Answer

we know that de-Broglie wave length = h / mv ==> v = h / m * lambda For electron , v = 6.6 x 10^-34 / 9.1 x 10^-31 * 0.18 x 10^-9 = 4.029 x 10^6 m/s For proton , v = 6.6 x 10^-34 / 1.67 x 10^-27 * 0.18 x 10^-9 = 2.195 x 10^3 m/s Therefore a) V = 0.5 m v^2 / q = 0.5 * 9.1 x 10^-31 * (4.029 x 10^6)^2 / 1.6 x 10^-19 = 46.16 V b) V = 0.5 m v^2 / q = 0.5 * 1.67 x 10^-27 * (2.195 x 10^3)^2 / 1.6 x 10^-19 = 0.025144 V

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