A moving hydrogen atom in its ground state collides with an identical ground-state hydrogen atom initially at rest. After the collision, both atoms are required to be in their first excited states. Assume equal atomic masses and use the non-relativistic threshold condition including momentum conservation. If the minimum incident kinetic energy is (N ÷ 10) eV, find N.
Physics · Atomic Structure and X-rays · atomic structure and bohr atomic model
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Question

A moving hydrogen atom in its ground state collides with an identical ground-state hydrogen atom initially at rest. After the collision, both atoms are required to be in their first excited states. Assume equal atomic masses and use the non-relativistic threshold condition including momentum conservation. If the minimum incident kinetic energy is (N ÷ 10) eV, find N.

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

G1 Physics · Accepted Answer

Each atom requires 10.2 eV to reach its first excited state. Total internal excitation required: ΔE(total) = 2×10.2 = 20.4 eV. For equal projectile and target masses, m ÷ M = 1. Therefore, K(threshold) = ΔE(total)[1+m ÷ M] = 20.4(1+1) = 40.8 eV. Thus, 40.8 eV = 408 ÷ 10 eV. Hence N = 408.