Calculate the momentum and the de Broglie wavelength in the following cases :
(i) an electron with kinetic energy 2 eV.
(ii) a bullet of 50g fired from rifle with a speed of 200 m/s
(iii) a 4000 kg car moving along the highways at 50 m/s
Hence show that the wave nature of matter is important at the atomic level but is not really relevant at macroscopic level.

Explanation

(i) Momentum of the electron is P `= sqrt(2mK)`
`= sqrt(2 xx 9.1 xx 10^(-31) xx 2 xx 1.6 xx 10^(-19)) = 7.63 xx 10^(-25)"kg ms"^(-1)`
Its de Broglie wavelength is
`lambda = (h)/(p) = (6.626 xx 10^(-34))/(7.63 xx 10^(-25)) = 0.868 xx 10^(-9)m = 8.68 Å`
(ii) Momentum of the bullet is
`p = mv = 0.050 xx 200 = "10 kg ms"^(-1)`
Its de Broglie wavelength is
`lambda = (h)/(p) = (6.626 xx 10^(-34))/(10) = 6.626 xx 10^(-33)`m
(iii) Momentum of the car is
`P = mv = 4000 xx 50 = 2 xx 10^(5)"kg ms"^(-1)`
Its de Broglie wavelength is
`lambda = (h)/(p) = (6.626 xx 10^(-34))/(2 xx 10^(5)) = 3.313 xx 10^(-39)`m
From these calculations, we notice that electron has significant value of de Broglie wavelength (`~~ 10^(-9)` m which can be measured from diffraction studies) but bullet and car have negligibly small de Broglie wavelengths associated with them (`~~ 10^(-33)m and 10^(-39)`m respectively, which are not measurable by any experiment). This implies that the wave nature of matter is important at the atomic level but it is not really relevant at the macrosopic level.