A) \[\frac{{{m}_{2}}}{{{m}_{1}}}\]
B) \[\frac{{{m}_{1}}}{{{m}_{2}}}\]
C) \[\frac{\sqrt{{{m}_{1}}}}{\sqrt{{{m}_{2}}}}\]
D) 1 : 1
Correct Answer: D
Solution :
By law of conservation of linear momentum \[{{m}_{1}}{{\upsilon }_{1}}={{m}_{2}}{{\upsilon }_{2}}\] So, \[{{m}_{1}}{{\upsilon }_{1}}={{m}_{2}}{{\upsilon }_{2}}\] Now, de-Broglie wavelength \[\lambda =\frac{h}{m\upsilon }\] \[\therefore \] \[\frac{{{\lambda }_{1}}}{{{\lambda }_{2}}}=\frac{{{m}_{2}}{{\upsilon }_{2}}}{{{m}_{1}}{{\upsilon }_{1}}}\] \[{{\lambda }_{1}}:{{\lambda }_{2}}=1:1\]
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