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 particle comes
P to rest, and the atom recoils and goes to its first excited

W state. The initial kinetic energy of the particle (in \( \mathrm{eV} \) ) is
\( \frac{N}{4} \). The value of \( N \) is (Given the mass of the hydrogen atom to be \( \left.1 \mathrm{GeV} / \mathrm{c}^{2}\right) \)
. [JEE Main-2020 (September)]
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