Question

Wavelength of a Bullet. Calculate the de Broglie wavelength of a 5.00-g bullet that is moving at 340 m/s. Will the bullet exhibit wavelike properties?

Short answer

The de Broglie wavelengths of the bullet is 3.9 x 10^-34 m but it won’t show any wavelike properties as the wavelength is too small to exhibit wave properties.

Step-by-step solution

Given Data

According to de Broglie, Light has dual nature as in some situations it behaves like waves and in others like particles. Electrons, which sometimes exhibits particle nature may also behave like wave in some situations.

When a particle acts like a wave, it carries a wavelength which is known as de Broglie wavelength.

The de Broglie wavelengths of bullet

Mass of bullet, m = 5 grams

Velocity of bullet, v = 340 m/s

The de Broglie wavelength of bullet is given by

$$\begin{gathered} \lambda =\frac{h}{p} \\ =\frac{h}{mv} \\ =\frac{6.62*{10}^{-34}Js}{\left(5*{10}^{-3}kg\right)\left(340m/s\right)} \\ =3.9*{10}^{-34}m \end{gathered}$$

Therefore, the de Broglie wavelengths of the bullet is 3.9 x 10^-34 m but it won’t show any wavelike properties as the wavelength is too small to exhibit wave properties.