A) 2 : 5
B) 3 : 4
C) 6 : 4
D) 5 : 2
Correct Answer: D
Solution :
[d] Given, \[{{v}_{A}}=0.1\text{ }m{{s}^{-1}}\]and \[{{v}_{B}}=0.05\text{ }m{{s}^{-1}}\]ms-1 also, \[{{m}_{B}}=5{{m}_{A}}\] de-Broglie wavelength, \[\lambda =\frac{h}{mv}\] \[\therefore \frac{{{\lambda }_{A}}}{{{\lambda }_{B}}}=\frac{h/{{m}_{A}}{{v}_{A}}}{h/{{m}_{B}}{{v}_{B}}}=\frac{{{m}_{B}}{{v}_{B}}}{{{m}_{A}}{{v}_{A}}}\] \[=\frac{5{{m}_{A}}\times 0.05}{{{m}_{A}}\times 0.1}=5\times 0.5=2.5=5\text{/}2\] \[\therefore {{\lambda }_{A}}:{{\lambda }_{B}}=5:2\]
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