Modern Physics 4 Question 2

2. 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 (Main 2019, 9 April II)

(a) λxλy

(b) λxλyλxλy

(c) λxλyλx+λy

(d) λx+λy

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Solution:

  1. Initially,

pxxpyy

We have, de-Broglie wavelengths associated with particles are

λx=hpx and λy=hpypx=hλx and py=hλy

Finally, particles collided to form a single particle.

As we know that linear momentum is conserved in collision, so

pp=|pxpy|pp=|hλxhλy|

So, de-Broglie wavelength of combined particle is

λp=h|pp|=h|hλxhλy|=h|hλyhλxλxλy|=λxλy|λxλy|



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