An electron X is accelerated from rest through a potential difference V. Another electron Y is accelerated from rest through a potential difference 2V. After acceleration, the de Broglie wavelength of X is λ_X and that of Y is λ_Y. The speeds reached by the electrons are well below that of the speed of light.

What is the ratio \(\frac{{{\lambda _{\rm{X}}}}}{{{\lambda _{\rm{Y}}}}}\)?

A. 2

B. \(\sqrt 2 \)

C. \(\frac{1}{2}\)

D. \(\frac{1}{{\sqrt 2 }}\)

B

This was a very good discriminator – but involved a lot of guessing for the weaker candidates.

Candidates should be familiar with the de Broglie wavelength increasing as the speed of the particle increases, so C and D can be eliminated immediately. And, in calculating the change in wavelength (which they do not need to do) the equation kinetic energy = potential energy will be used. This involves the square of the velocity, hence B must be true.