A) 3 : 1
B) 9 : 1
C) 5 : 12
D) 16 : 9
Correct Answer: D
Solution :
[d] de Broglie wavelength \[\lambda =\frac{h}{mv}\] \[\frac{{{\lambda }_{1}}}{{{\lambda }_{2}}}=\frac{{{m}_{2}}{{v}_{2}}}{{{m}_{1}}{{v}_{1}}};\frac{1}{4}=\frac{1}{9}\times \frac{{{v}_{2}}}{{{v}_{1}}}\] \[\frac{{{v}_{2}}}{{{v}_{1}}}=\frac{9}{4};\frac{{{v}_{1}}}{{{v}_{2}}}=\frac{4}{9}\] \[KE=\frac{1}{2}m{{v}^{2}}\] \[\frac{K{{E}_{1}}}{K{{E}_{2}}}=\frac{{{m}_{1}}}{{{m}_{2}}}\times \frac{{{v}_{l}}^{2}}{{{v}_{2}}^{2}}=\frac{9}{1}\times {{\left( \frac{4}{9} \right)}^{2}}=\frac{16}{9}\]
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