What is the wavelength of an electron which has been accelerated from rest through a potential difference of 20 V?

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QUESTION: Approximately what is the "de Broglie" wavelength of an electron that has been accelerated through a potential difference of = 150 V? (The mass of an electron = 9.11 x 10-31 kg.) Possible answers: (a) 0.1 nm (b) 1 nm (c) 10 nm (d) 100 nm (e) 1000 nm The kinetic energy of an electron accelerated through a potential difference of V volts is given by the equation:

� mv2 = eV where e is the electron charge (1.6x10-19 C) [You must be given the electron charge and Planck's constant in order to answer this question].

and so v = √(2eV/m) = 7.26x106 m/s

Therefore: wavelength = h/mv = h/[9.11x10- 31x7.26x106] = 1x10-10 = 0.1 nm

The correct answer is (a)