An electron accelerated from rest through a potential difference V has de Broglie wavelength λ. What is the wavelength of an electron accelerated from rest through a potential difference of 2V? 

A. 2λ

B. \(\frac{\lambda }{2}\)

C. \(\sqrt {2\lambda } \)

D. \(\frac{\lambda }{{\sqrt 2 }}\)

D

The responses showed that the majority of the candidates understood that the wavelength gets smaller with increasing speed of the electron (responses B and D). However they failed to realize that the energy given to the particle is proportional to the square of the velocity. Hence the factor of √2 is necessary when considering the momentum.