An \[\alpha \]-particle having a de-Broglie wavelength \[{{\lambda }_{i}}\] collides with a stationary carbon nucleus. The \[\alpha \]-particle moves off in a different direction as shown below. 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. \[{{\lambda }_{i}}={{\lambda }_{e}}\]