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

Question

According to de Broglie, 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.

✓

Answer

Given, $m =100 g=0.1 kg$.
Velocity, $v =100 km / hr =\frac{100 \times 1000}{60 \times 60}=\frac{10000}{36} ms^{-1}$.
According to be Broglie, Wavelength $\lambda=\frac{h}{m v}$; Where $h =6.626 \times 10^{-34} Js$.
Now, Put the values in above equation, we get
$
\begin{aligned}
& \lambda=\frac{6.626 \times 10^{-34} Js}{0.1 kg \times \frac{1000}{36} ms^{-1}}=6.626 \times 10^{-36} \times 36 m \\
& \lambda=238.5 \times 10^{-36} m
\end{aligned}
$
Since the wavelength is too small to be detected, so, it does not show wave nature.

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