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Wavelength of an accelerated electron

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


Answer:

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)
 
 
 
© Keith Gibbs 2013