A beam of electrons is accelerated from rest through a potential difference $V$. The de Broglie wavelength of the electrons is $\lambda$. For electrons accelerated through a potential difference of $2V$ the de Broglie wavelength is

A.     $2\lambda$

B.     $\sqrt {2\lambda }$

C.     $\frac{\lambda }{2}$

D.     $\frac{\lambda }{{\sqrt 2 }}$

D