A neutral helium atom of mass approximately 4u moves toward a stationary ground-state hydrogen atom of mass approximately u. During an inelastic collision, the hydrogen atom is to be excited to its first excited state. Using the non-relativistic threshold condition and neglecting electron masses in the atomic masses, if the minimum helium kinetic energy is N eV, find N.
Physics · Atomic Structure and X-rays · atomic structure and bohr atomic model
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Question

A neutral helium atom of mass approximately 4u moves toward a stationary ground-state hydrogen atom of mass approximately u. During an inelastic collision, the hydrogen atom is to be excited to its first excited state. Using the non-relativistic threshold condition and neglecting electron masses in the atomic masses, if the minimum helium kinetic energy is N eV, find N.

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

G1 Physics · Accepted Answer

Hydrogen first-excitation energy is ΔE = 10.2 eV. Projectile mass: m = 4u. Target mass: M = u. Threshold energy: K(threshold) = ΔE[1+m ÷ M] = 10.2[1+4] = 51 eV. Hence N = 51.