Quantum effects are only visible when the de Broglie wavelength of a particle is

Question

Quantum effects are only visible when the de Broglie wavelength of a particle is comparable to or larger than a key dimension. We might naively consider an electron transferring from n donor to acceptor across a protein as a free electron moving through space. Assume an electron travels 50 A with a kinetic energy of 41.K4 kJ mol^-1. Can we think of the electron as classical, or do we have to treat it quantum mechanically? At 0.4184 kJ mol^-1s? Repeat the above calculation under the same conditions, but for a proton transferring.

Explanation / Answer

If kinetic energy is 0.4184 kJ/mol

K.E = 1/2 mv2

0.4184 = 1/2 (9.1*10-31) v2

v = 9.590*1014 m

De-Broglie's wave - particle equation,

lambda = h / (mv)

= 6.625*10-34 / (9.1*10-31*9.590*1014)

= 7.591 * 10-19 m

As the value of wave length is too low the wave nature can not be observe. Hence electron is thought as classical mechanics.

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