A proton collides with a stationary hydrogen atom initially in its ground state. Assume the projectile proton and the hydrogen atom have approximately equal masses. Because momentum must also be conserved, the laboratory threshold kinetic energy is greater than the 10.2 eV internal excitation energy. If the minimum proton kinetic energy needed to excite the hydrogen atom to its first excited state is (N ÷ 10) eV, find N.
Physics · Atomic Structure and X-rays · atomic structure and bohr atomic model
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Question

A proton collides with a stationary hydrogen atom initially in its ground state. Assume the projectile proton and the hydrogen atom have approximately equal masses. Because momentum must also be conserved, the laboratory threshold kinetic energy is greater than the 10.2 eV internal excitation energy. If the minimum proton kinetic energy needed to excite the hydrogen atom to its first excited state is (N ÷ 10) eV, find N.

Physics · Atomic Structure and X-rays · atomic structure and bohr atomic model

G1 Physics · Accepted Answer

The required internal excitation is ΔE = 10.2 eV. For an endoergic collision in which a projectile of mass m strikes a stationary target of mass M, the non-relativistic threshold laboratory energy is K(threshold) = ΔE[1+m ÷ M]. Here, m ≈ M. Therefore, K(threshold) = 10.2(1+1) = 20.4 eV. Thus, 20.4 eV = 204 ÷ 10 eV. Hence N = 204.