From quantum mechanical perspective, molecules have structures that can be repre

Question

From quantum mechanical perspective, molecules have structures that can be represented as circles. Chlorophyll and hemoglobin are very good examples of these kind of molecules. Suppose that an electron of wavelength lambda travels around a molecule of radius R. Determine the fundamental frequency of the electron? One wavelength of the electron must fit into the circumfernce of R. Given that the momentum of any particle is given by p = h/lambda where h is Plank's constant, what is the momentum of the electron? Then what is the kinetic energy of an electron of wavelength lambda?

Explanation / Answer

let m is the mass of electron.

given p = h/lamda

m*v = h/R

v = h/(m*R)

time period of elctron, T = 2*pi*R/v

= 2*pi*R/(h/(m*R))

= 2*pi*m*R^2/h

fundamental frequency, f = 1/T

= h/(2*pi*m*R^2)

momentum of the elctron, p = h/R

kinetic energy of the elctron, KE = p^2/(2*m)

= (h/R)^2/(2*m)

= h^2/(2*m*R^2)

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