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:- (a) λx - λy (b) (λxλy)/(|λx-λy|) (c) λx + λy (d) (λxλy)/(λx+λy)

A particle 'P' is formed due to a completely inelastic collision of… | JEE Main 2019 (9 Apr, Shift 2)

Q124JEE Main 2019 · 9 APR · SHIFT 2Difficult

Matter Waves: de Broglie Wavelength

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 :-

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Answer: (b)

Opposite directions: $p = |p_x - p_y| = h\left|\dfrac{1}{\lambda_x} - \dfrac{1}{\lambda_y}\right|$
$\lambda_P = \dfrac{h}{p} = \dfrac{\lambda_x\lambda_y}{|\lambda_x - \lambda_y|}$
So the answer is (b).

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