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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 N/4 . The value of N is (given the mass of the hydrogen atom to be 1 GeV/c2) ___________. (in integers)
Correct answer is '57'. Can you explain this answer?
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A particle of mass 200 MeV/c2 collides with a hydrogen atom at rest. S...

Given Data:
- Mass of the particle = 200 MeV/c²
- Mass of the hydrogen atom = 1 GeV/c²
- Kinetic energy of the particle = N/4 eV

Calculating Initial Kinetic Energy:
- Initial kinetic energy of the particle = Final kinetic energy of the hydrogen atom
- 1/2 * mass of particle * velocity² = 1/2 * mass of hydrogen atom * velocity² + energy required for excitation
- 200 * v² = 1000 * v² + 13.6 eV (energy required for excitation)
- 800 * v² = 13.6 eV
- v² = 13.6 / 800 = 0.017 eV
- v = √0.017 ≈ 0.13 c

Calculating Kinetic Energy (N):
- Initial kinetic energy of the particle = 1/2 * mass of particle * velocity²
- N/4 = 1/2 * 200 * (0.13)²
- N = 4 * 1/2 * 200 * 0.0169 ≈ 57

Therefore, the value of N is 57.
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Community Answer
A particle of mass 200 MeV/c2 collides with a hydrogen atom at rest. S...
M0 = 200 MeV/c2; m = 1 GeV/c2
Initial velocity = v0
Mv0 = mv
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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 N/4 . The value of N is (given the mass of the hydrogen atom to be 1 GeV/c2) ___________. (in integers)Correct answer is '57'. Can you explain this answer?
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