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  • A particle A with a mass mA is moving with a velocity v and hits a particle B (mass mB) at rest (one dimensional motion). Find the change in the de Broglie wavelength of the particle A. Treat the collision as elastic.

A particle A with a mass mA is moving with a velocity v and hits a particle B (mass mB) at rest (one dimensional motion). Find the change in the de Broglie wavelength of the particle A. Treat the collision as elastic.

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When the collision is elastic, law of conservation of momentum is followed.

m_{A}v+m_{B}0=m_{A}v_{1}+m_{B}v_{2}\\ m_{A}\left ( v-v_{1} \right )=m_{B}v_{2}\\ \frac{1}{2}m_{A}v_{2}= \frac{1}{2}m_{A}v_{1}^{2}+\frac{1}{2}m_{B}v_{2}^{2}\\ v_{1}=\frac{m_{A}-m_{B}}{\left ( m_{A}-m_{B} \right )}v\;\;\;v_{2}=\frac{2m_{A}}{\left ( m_{A}-m_{B} \right )}v\\\\ \lambda_{initial}=\frac{h}{m_{A}v}\\ \lambda_{final}=\frac{h}{m_{A}v_{1}}\\ \Delta \lambda=\lambda_{final}-\lambda_{initial}=\frac{h}{m_{A}v}\left [ \frac{m_{A}+m_{B}}{m_{A}-m_{B}}-1 \right ]

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