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The reflection of hydrogen atoms from lithium fluoride

1930; Elsevier BV; Volume: 210; Issue: 2 Linguagem: Inglês

10.1016/s0016-0032(30)90738-7

1879-2693

Thomas H. Johnson,

Geophysics and Sensor Technology

The paper describes the phenomena associated with the reflection of a sharply defined beam of hydrogen atoms from a crystal of LiF. Of primary interest is the fact that the atoms show interference effects in agreement with the wave mechanics theory and plane grating diffraction patterns are photographed. Evidence of the thermal agitation of the surface ions is obtained from the diffuse reflection with surrounds the specular beam. The Schrödinger wave equation for the motion of a free particle of mass m is ▽2ψ − 4πmih∂ψ∂t = 0 (I). The solution of this equation corresponding to the kinetic energy mv22 is ψ = Ae2πi(vt−σxx−σyy−σxz), (2) where v  mv22and σ mvh. The motion of such a particle should have the characteristics of a plane wave of frequency ν and wave-length λ = 1σ. The experiments of various investigators1 have shown the validity of the wave theory of the motion of the free electron and have given values of the wave-length in agreement with the theory. The free motion of atoms, ions and molecules should likewise have wave characteristics. In the case of the hydrogen atom, as the simplest example, the complete wave equation may be written in the form Im ▽2 x,y,zψ + Iμ ▽2η,μζψ −8π2μℓψmh2η2 + μ2 + ζ2− 4πih∂ψ∂t = 0, (3) where x, y, z, are the coördinates of the center of mass of the atom and ξ, η, ζ the coördinates of the electron with respect to the center of mass. If m− and m+ are the masses of electron and proton, m and μ have the significance m = m− + m+and Iμ = Im− + Im+. Equation (3) is solved by ψ = U1(x,y,z) U2(η, ν ζ) ℓ2πiEth, where E may have a continuous set of values and represents the total energy. U1 and U2 must satisfy the equations ▽12U1 + 8π2mβU1h2 = 0, (4) and ▽22U2 + 8π2μh2 (α − μℓmη2 + ν2 + ζ2)U2 = 0 (5), where α + β + E.