According to de Broglie, the matter should exhibit dual behaviour, that is both particle and wave-like properties. However, a cricket ball of mass 100 g does not move like a wave when it is thrown by a bowler at a speed of 100 km/h. Calculate the wavelength of the ball and explain why it does not show wave nature.

Question

According to de Broglie, the matter should exhibit dual behaviour, that is both particle and wave-like properties. However, a cricket ball of mass 100 g does not move like a wave when it is thrown by a bowler at a speed of 100 km/h. Calculate the wavelength of the ball and explain why it does not show wave nature.

Philoid · Accepted Answer

According to de-Broglie,

λ = h / mv ,

where λ is the wavelength of the particle-wave, m and v are the mass and velocity of the particle respectively and h = Planck’s constant = 6.626 X 10^-34 J.s

hence, in this case, λ =

now, m = 100g = 0.1 kg and

v=100km/h = 100 X1000/ 60X60 = 1000/36 m/s

λ =

= 238.5 X 10^-36 m^-1

The range of wavelength is very small here (10 ^-36), therefore the wave nature of the ball cannot be detected.