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 $$1$$ $$GeV/c2$$ $$)________________$$

Question

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  $$1$$ $$GeV/c2$$ $$)________________$$

Infinity Learn · Accepted Answer

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 △$$E=10.2eV$$⇒$$410mv2=10.2eV$$​⇒$$12mv2=12.75eV=514eV$$

Bohr's atom model

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