A hydrogen atom with kinetic energy 125 eV makes a head-on elastic collision with a stationary helium atom. Approximate their masses as u and 4u respectively. If the maximum kinetic energy transferred to the helium atom is N eV, find N.
Physics · Atomic Structure and X-rays · atomic structure and bohr atomic model
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Question

A hydrogen atom with kinetic energy 125 eV makes a head-on elastic collision with a stationary helium atom. Approximate their masses as u and 4u respectively. If the maximum kinetic energy transferred to the helium atom is N eV, find N.

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

G1 Physics · Accepted Answer

Maximum transferred fraction: f = 4mM ÷ (m+M)². Here, m = u, M = 4u. Thus, f = 4×1×4 ÷ 5² = 16 ÷ 25. Transferred energy: K_T = 125×16 ÷ 25 = 80 eV. Hence N = 80.