A) \[2\sqrt{2}:1\]
B) \[1:2\]
C) \[2:1\]
D) \[1:1\]
Correct Answer: A
Solution :
de-Broglie hypothesis states that all matter has wave like nature and that the wavelength \[(\lambda )\] and momentum (p) of a particle are related by \[\lambda =\frac{h}{p}\] Momentum (p) is related to energy (qV) as \[p=\sqrt{2m\,(qV)}\] where m is mass : \[\therefore \] \[\lambda =\frac{h}{\sqrt{2\,m\,(qV)}}\] \[\Rightarrow \] \[\frac{{{\lambda }_{p}}}{{{\lambda }_{\alpha }}}=\sqrt{\frac{{{m}_{\alpha }}\,{{q}_{\alpha }}}{{{m}_{p}}\,{{q}_{p}}}}=\sqrt{\frac{4\times 2}{1\times 1}}=\frac{2\sqrt{2}}{1}\]
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