A) 14.14
B) 0.07
C) 4.47
D) 10.00
Correct Answer: A
Solution :
For particle A \[{{m}_{1}}=m,{{q}_{1}}=q;{{V}_{1}}=50\,V\] \[{{\lambda }_{A}}=\frac{h}{\sqrt{2{{m}_{1}}{{q}_{1}}{{V}_{1}}}}\] ?.(i) For particle B \[{{m}_{2}}=4m,{{q}_{2}}=q;{{V}_{2}}=2500\,V\] \[{{\lambda }_{B}}=\frac{h}{\sqrt{2{{m}_{2}}{{q}_{2}}{{V}_{2}}}}\] ...(ii) Dividing eqn. (i) by (ii), \[\frac{{{\lambda }_{A}}}{{{\lambda }_{B}}}=\sqrt{\frac{{{m}_{2}}{{q}_{2}}{{v}_{2}}}{{{m}_{1}}{{q}_{1}}{{v}_{1}}}}=\sqrt{\frac{4m\times q\times 2500}{m\times q\times 50}}\] \[\frac{{{\lambda }_{A}}}{{{\lambda }_{B}}}=\sqrt{\frac{4\times 2500}{50}}=14.14\]
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