Two particles move at right angle to each other. Their de Broglie wavelengths are λ _ 1 and λ _ 2 respectively. The particles suffer perfectly inelastic collision. The de Broglie wavelength λ of the final particle, is

Correct answer: D. 1 λ ^ 2 = 1 λ _ 1 ^ 2 + 1 λ _ 2 ^ 2 → P _ 1 = h λ _ 1 ^ i , → P _ 2 = h λ _ 2 ^ j → P = → P _ 1 + → P _ 2 = h λ _ 1 ^ i + h λ _ 2 ^ j | → P | = h 1 λ _ 1 ^ 2 + 1 λ _ 2 ^ 2 (h)/(λ) = h 1 λ _ 1 ^ 2 + 1 λ _ 2 ^ 2 1 λ ^ 2 = 1 λ _ 1 ^ 2 + 1 λ _ 2 ^ 2

JEE Main 20198 AprilMorning Shift

Exam: JEE Main
Year: 2019
Date: 8 April
Shift: Morning Shift
Subject: Physics
Chapter: Dual Nature of Matter

JEE Main 2019 · 8 April · Morning Shift · Physics · Dual Nature of Matter

Two particles move at right angle to each other. Their de Broglie...

Two particles move at right angle to each other. Their de Broglie wavelengths are

{\lambda}_{1}

and

{\lambda}_{2}

respectively. The particles suffer perfectly inelastic collision. The de Broglie wavelength

\lambda

of the final particle, is given by:

Options

A $\dfrac{2}{\lambda} = \dfrac{1}{{\lambda}_{1}} + \dfrac{1}{{\lambda}_{2}}$
B $\lambda = \dfrac{{\lambda}_{1} + {\lambda}_{2}}{2}$
C $\lambda = \sqrt{{\lambda}_{1}{\lambda}_{2}}$
D $\dfrac{1}{{\lambda}^{2}} = \dfrac{1}{{\lambda}_{1}^{2}} + \dfrac{1}{{\lambda}_{2}^{2}}$

Correct answer

D. $\dfrac{1}{{\lambda}^{2}} = \dfrac{1}{{\lambda}_{1}^{2}} + \dfrac{1}{{\lambda}_{2}^{2}}$

Step-by-step solution

\overset{\to}{{P}_{1}} = \dfrac{h}{{\lambda}_{1}}\overset{^}{i}\text{,}\overset{\to}{{P}_{2}} = \dfrac{h}{{\lambda}_{2}}\overset{^}{j}

<br/>

\overset{\to}{P} = \overset{\to}{{P}_{1}} + \overset{\to}{{P}_{2}} = \dfrac{h}{{\lambda}_{1}}\overset{^}{i} + \dfrac{h}{{\lambda}_{2}}\overset{^}{j}

<br/>\left|\overset{\to}{P}\right| = h\sqrt{\dfrac{1}{{\lambda}_{1}^{2}} + \dfrac{1}{{\lambda}_{2}^{2}}}

\dfrac{h}{\lambda} = h\sqrt{\dfrac{1}{{\lambda}_{1}^{2}} + \dfrac{1}{{\lambda}_{2}^{2}}}

\dfrac{1}{{\lambda}^{2}} = \dfrac{1}{{\lambda}_{1}^{2}} + \dfrac{1}{{\lambda}_{2}^{2}}

Practice Dual Nature of Matter on Quantrex Academy →

More from Dual Nature of Matter

K_1 and K_2 be the maximum kinetic energies of photoelectrons emitted from a surface of a… JEE Main 2026 The de Broglie wavelength for an electron accelerated through the potential difference of… JEE Main 2026 Given below are two statements: one is labelled as Assertion (A) and the other is… JEE Main 2026 An electron is travelling with a velocity v in free space and when it enters a medium… JEE Main 2026 An electron of mass m is moving in an electric field E = -2E_0 i ( E_0 = constant > 0 )… JEE Main 2026 Light source having wavelength 331 nm is used to generate photo-electrons whose stopping… JEE Main 2026 Match the LIST-I with LIST-II List-I List-II A. Planck's constant I. ML^2T^ -2 B.… JEE Main 2026 The de Broglie wavelength associated with an electron accelerated through a potential… JEE Main 2026 Full Dual Nature of Matter list All JEE Main PYQs