The wave function of a free electron is $\Psi$(x)= A sin (4.72 x 10¹⁰ x),where x is in m.The magnitude of the momentum of the electron is A)5.96 * 10^-26 kg m/s. B)4.98 * 10^-24 kg m/s. C)2.95 * 10^-20 kg m/s. D)1.09 * 10^-18 kg m/s.

Question

Quizplus · Accepted Answer

The momentum of a particle is p = h/λ, where h is the Planck constant and λ is the wavelength. In this case, the wavelength of the electron is given by λ = 2π/k, where k is the wave number. The wave number is related to the magnitude of the momentum by k = p/h.

The wave function given in the problem is sin (4.72 x 10^6 x), where the units of x are meters. The wave number is therefore k = 4.72 x 10^6 m^-1. The wavelength is λ = 2π/k = 1.33 x 10^-6 m.

Finally, we can calculate the momentum as p = h/λ = 4.98 x 10^-24 kg m/s. This matches answer choice B.

The Wave Function of a Free Electron Is Ψ\PsiΨ (X)= a Sin (4

The Wave Function of a Free Electron Is $\Psi$ (X)= a Sin (4