After the collision, the de Broglie wavelengths of the \[\alpha \]-particle and the carbon nucleus are \[{{\lambda }_{f}}\] and \[{{\lambda }_{e}}\] respectively. Which of the following relations about de Broglie wavelengths is correct
A) \[{{\lambda }_{i}}<{{\lambda }_{f}}\]
B) \[{{\lambda }_{i}}>{{\lambda }_{f}}\]
C) \[{{\lambda }_{f}}={{\lambda }_{i}}\]
D) \[{{\lambda }_{i}}={{\lambda }_{e}}\]
Correct Answer: A
Solution :
[a] Final speed of \[\alpha \]-particle will be less than the initial speed therefore, \[\left( \frac{h}{{{\lambda }_{f}}} \right)<\left( \frac{h}{{{\lambda }_{i}}} \right)\text{ or }{{\lambda }_{f}}>{{\lambda }_{i}}\]
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