A particle of mass 200 MeV/c2 collides with a hydrogen atom at rest. Soon after the collision the particle comes to rest, and the atom recoils and goes to its first excited state. The initial kinetic energy of the particle in eV is N4. The value of N is: (Given the mass of the hydrogen atom to be  1 GeV/c2 )________________

Given : mp=200 ×106eV/c2  and mH=109eV/c2​Dividing, mHmp=109200 ×106=5​⇒mH=5mp​Mass of hydrogen atom is 5 times mass of colliding particle .       Conservation of Momentum, ​mpvp=mHvH​⇒mv=5mvH​⇒vH=v5Loss in energy=Ki−Kf =12mv2−125mv52=410mv2This energy goes into exciting electron from n=1 to n=2 means △E=10.2eV⇒410mv2=10.2eV​⇒12mv2=12.75eV=514eV