A) \[{{m}_{1}}/{{m}_{2}}\]
B) \[{{m}_{2}}/{{m}_{1}}\]
C) 1.0
D) \[\sqrt{{{m}_{2}}}/\sqrt{{{m}_{1}}}\]
Correct Answer: C
Solution :
By law of conservation of momentum \[0={{m}_{1}}\overrightarrow{{{v}_{1}}}+{{m}_{2}}\overrightarrow{{{v}_{2}}}\Rightarrow {{m}_{1}}\overrightarrow{{{v}_{1}}}=-{{m}_{2}}\overrightarrow{{{v}_{2}}}\] ? ve sign indicates that both he particles are moving in opposite direction. Now de-Broglie wavelengths \[{{\lambda }_{1}}=\frac{h}{{{m}_{1}}{{v}_{1}}}\] and \[{{\lambda }_{2}}=\frac{h}{{{m}_{2}}{{v}_{2}}}\]; \[\therefore \ \frac{{{\lambda }_{1}}}{{{\lambda }_{2}}}=\frac{{{m}_{2}}{{v}_{2}}}{{{m}_{1}}{{v}_{1}}}=1\]
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