A) \[2{{\lambda }_{A}},{{\lambda }_{A}}\]
B) \[{{\lambda }_{A}},2{{\lambda }_{A}}\]
C) \[{{\lambda }_{A}},\frac{{{\lambda }_{A}}}{2}\]
D) \[\frac{{{\lambda }_{A}}}{2},{{\lambda }_{A}}\]
Correct Answer: D
Solution :
let mass of B and C is m each. By momentum conservation \[2m{{\text{v}}_{0}}=m\text{v}-\frac{m\text{v}}{2}\] \[\text{v}-4{{\text{v}}_{0}}\] \[{{p}_{A}}\text{=2m}{{\text{v}}_{0}}\,\,\,\,\,\,\,{{p}_{B}}\text{=4m}{{\text{v}}_{0}}\,\,\,\,\,\,\,\,{{p}_{c}}\text{=2m}{{\text{v}}_{0}}\] De-Broglie wavelength \[\lambda =\frac{h}{p}\] \[{{\lambda }_{A}}=\frac{h}{2m{{\text{v}}_{0}}};{{\lambda }_{B}}=\frac{h}{4m{{\text{v}}_{0}}};{{\lambda }_{C}}=\frac{h}{2m{{\text{v}}_{0}}}\]You need to login to perform this action.
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