A particle 'P' is formed due to a completely inelastic collision of particles 'x' and 'y' having de-Broglie wavelengths 'λx' and 'λy' respectively. If x and y were moving in opposite directions, then the de-Broglie wavelength of 'P' is:

Engineering

Physics

de Broglie Hypothesis and Dual Nature

Question

A particle 'P' is formed due to a completely inelastic collision of particles 'x' and 'y' having de-Broglie wavelengths 'λ_x' and 'λ_y' respectively. If x and y were moving in opposite directions, then the de-Broglie wavelength of 'P' is:

λ_x + λ_y

$\frac{λ_{x} λ_{y}}{λ_{x} + λ_{y}}$

$\frac{λ_{x} λ_{y}}{| λ_{x} - λ_{y} |}$

λ_x – λ_y

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Conservation of momentum

${\vec{p}}_{x} + {\vec{p}}_{y} = {\vec{p}}_{final}$

m_xv_x – m_xv_x = (m_x + m_y) V

$\frac{h}{λ_{x}} - \frac{h}{λ_{y}} = \frac{h}{λ}$

$\Rightarrow λ = \frac{λ_{x} λ_{y}}{| λ_{x} - λ_{y} |}$