A particle of mass \( 200 \mathrm{MeV} / \mathrm{c}^{2} \) collides with a hydrogen atom at rest...

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A particle of mass \( 200 \mathrm{MeV} / \mathrm{c}^{2} \) collides with a hydrogen atom at rest. Soon after the collision the
\( \mathrm{P} \)
particle comes to rest, and the atom recoils and goes
W
to its first excited state. The initial kinetic energy of the particle (in \( \mathrm{eV} \) ) is \( N / 4 \). The value of \( N \) is . (Given the mass of the hydrogen atom to be \( 1 \mathrm{GeV} / \mathrm{c}^{2} \) )
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