Find the condition under which de Broglie wave-length of a moving electron becomes twice that of a moving proton? Givenn that a proton is 1836 times heavier than an electron.

Explanation

`lamda_(e)=(h)/(m_(e)v_(e)) and lamda_(p)=(h)/(m_(p)v_(p))`
Since, `lamda_(e)=2xxlamda_(p)" "therefore (h)/(m_(e)v_(e))=2xx(h)/(m_(p)v_(p))`
or, `2xxm_(e)v_(e)=m_(p)v_(p)`
or, `v_(e)=(m_(p)v_(p))/(2m_(e))=(v_(p))/(2)xx(m_(p))/(m_(e))=(v_(p))/(2)xx1836=918v_(p)`
i.e., `v_(e)=918v_(p)`, this is the necessary condition.