Physics Circle home Student Login

Home›Chapters›Dual Nature of Radiation and Matter PYQs›Matter Waves: de Broglie Wavelength›Question 132

JEE Main 2017 · Matter Waves: de Broglie Wavelength

Matter Waves: de Broglie Wavelength question from JEE Main 2017

Q132JEE Main 2017Medium

Matter Waves: de Broglie Wavelength

A particle A of mass m and initial velocity v collides with a particle B of mass m/2 which is at rest. The collision is head on, and elastic. The ratio of the de-Broglie wavelengths λA\lambda_A to λB\lambda_B after the collision is:

Show answer and solution

Answer: (b)

  1. Elastic head-on, B at rest: vA=m−m/2m+m/2v=v3v_A = \dfrac{m - m/2}{m + m/2}v = \dfrac{v}{3}, vB=2mm+m/2v=4v3v_B = \dfrac{2m}{m+m/2}v = \dfrac{4v}{3}.
  2. pA=mv3p_A = \dfrac{mv}{3}, pB=m2⋅4v3=2mv3p_B = \dfrac{m}{2}\cdot\dfrac{4v}{3} = \dfrac{2mv}{3}
  3. λAλB=pBpA=2\dfrac{\lambda_A}{\lambda_B} = \dfrac{p_B}{p_A} = 2
  4. So the answer is (b).
Report a mistake

More questions on Matter Waves: de Broglie Wavelength