Dual Nature of Matter

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71 of 200

Question 71 of 200

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

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Answer: (C) λxλy∣λx−λy∣\dfrac{{\lambda }_{x}{\lambda }_{y}}{\left|{\lambda }_{x}-{\lambda }_{y}\right|}

hλ=∣hλx−hλy∣\dfrac{h}{\lambda }=\left|\dfrac{h}{{\lambda }_{x}}-\dfrac{h}{{\lambda }_{y}}\right|
1λ=∣1λx−1λy∣\dfrac{1}{\lambda }=\left|\dfrac{1}{{\lambda }_{x}}-\dfrac{1}{{\lambda }_{y}}\right|
λ=λxλy∣λx−λy∣\lambda =\dfrac{{\lambda }_{x}{\lambda }_{y}}{\left|{\lambda }_{x}-{\lambda }_{y}\right|}

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