QJEEM19Phf859: JEE Main 2019 Physics - Class 12 JEEM19Phf859 Solution: A particle 'P' is formed due to a completely inelastic…

Question

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A particle 'P' is formed due to a completely inelastic collision of particles 'x' and 'y' having de-Broglie wavelengths '

\lambda

_x' and '

\lambda

_y' respectively. If x and y were moving in opposite directions, then the de-Broglie wavelength of 'P' is :-

A ${\lambda _x} - {\lambda _y}$
B ${{{\lambda _x}{\lambda _y}} \over {\left| {{\lambda _x} - {\lambda _y}} \right|}}$
C ${\lambda _x} + {\lambda _y}$
D ${{{\lambda _x}{\lambda _y}} \over {{\lambda _x} + {\lambda _y}}}$

Accepted Answer

Conservation of momentum

\overrightarrow {{p_x}} + \overrightarrow {{p_y}} = {\overrightarrow p _{final}}

m_xv_x – m_yv_y = (m_x + m_y) V

{h \over {{\lambda _x}}} - {h \over {{\lambda _y}}} = {h \over \lambda }

\Rightarrow \lambda = {{{\lambda _x}{\lambda _y}} \over {\left| {{\lambda _x} - {\lambda _y}} \right|}}

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