Two particles A and B of de-broglie wavelength `lambda_(1) and lambda_(2)` combine to from a particle C. The process conserves momentum. Find the de-Broglie wavelength of the particle C. (The motion is one dimensional).

Options

A. `lamda_(A)`
B. `lamda_(A)lamda_(B)//(lamda_(A)+lamda_(B))`
C. `lamda_(A)lamda_(B)//|lamda_(A)-lamda_(B)|`
D. both (b) and ( c)

Answer

D

Explanation

(d) : For one dimensional motion,
`vec(P_(C))=vec(P_(A))+vec(P_(B))`
If `P_(A),P_(B)gt0orP_(A),P_(B)lt0,i.e.P_(A)andP_(B)` are in same direction).
`P_(C)=P_(A)+P_(B)`
`(h)/(lamda_(C))=(h)/(lamda_(A))+(h)/(lamda_(C))=(h)/(lamda_(B))=h((lamda_(A)+lamda_(B))/(lamda_(A)lamda_(B)))rArrlamda_(C)=(lamda_(A)lamda_(B))/(lamda_(A)+lamda_(B))`
If `P_(A)gt0,P_(B)lt0 or P_(A)lt0,P_(B)gt0" "(P_(A)andP_(B)"are in opposite direction")`
`P_(C)=|P_(A)-P_(B)|`
`(h)/(lamda_(C))=|(h)/(lamda_(A))-(h)/(lamda_(B))|=(h|lamda_(A)-lamda_(B)|)/(lamda_(A)lamda_(B))`
`lamda_(C)=(lamda_(A)lamda_(B))/(|lamda_(A)-lamda_(B)|)`