According to de Broglie, matter should exhibit dual behaviour, th…

Question

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

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Answer

de Broglie equation,
$\lambda=\frac{\text{h}}{\text{mc}},\text{m}=100\text{g}=\frac{100}{1000}=0.1\text{kg},$
Velocity of cricket ball c,
$=100\text{km/ h}$
$=\frac{100\times1000\text{m}}{60\times60\text{s}}=-\frac{1000}{36}\text{ms}^{-1},$
Planck's constant, $\text{h}=6.626\times10^{-34}\text{Js}$
Wavelength,
$\lambda=\frac{6.626\times10^{-34}\text{Js}}{0.1\text{kg}\times\frac{1000}{36}\text{ms}^{-1}}=6.626\times10^{-36}\times36\text{m}$
$\lambda=2.385\times10^{-34}\text{m}$
Since mass of the ball is large, therefore, $'\lambda'$ is very small, the wave nature cannot be observed.

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