Two particles of masses m1, m2 move with initial velocities u1 and u2. On collision, one of the particles gets excited to a higher level, after absorbing energy ε. If the final velocities of the particles are v1 and v2, then we must have:

Using energy conservation principle:
Initial energy is only in the form of kinetic energy = 1/2m1u1² + 1/2m2u2².. (i)
Final energy is in the form of kinetic energy and potential energy (excitation energy) = 1/2m1v1² + 1/2m2v2² + ε.. (ii)
Equating (i) and (ii):
1/2m1u1² + 1/2m2u2² = 1/2m1v1² + 1/2m2v2² + ε
1/2m1u1² + 1/2m2u2² - ε = 1/2m1v1² + 1/2m2v2²
Hence, the correct answer is option A.