(a)
Hint: \(\lambda=\frac{h}{mv}\)

Step 1: Find the wavelength of the bullet.
Mass of the bullet, m = 0.040 kg
Speed of the bullet, v = 1.0 km/s = 1000 m/s
Planck's constant, h =6.6 x ${10}^{-34}$ Js
De Broglie wavelength of the bullet is given by the relation:
$\begin{array}{l}\lambda =\frac{h}{mv}\\ =\frac{6.6\times {10}^{-34}}{0.040\times 1000}=1.65\times {10}^{-35}m\end{array}$

(b)
Hint: \(\lambda=\frac{h}{mv}\)

Step 1: Find the wavelength of the ball.
Mass of the ball, m = 0.060 kg
Speed of the ball, v = 1.0 m/s
De Broglie wavelength of the ball is given by the relation:

$\begin{array}{l}\lambda =\frac{h}{mv}\\ =\frac{6.6\times {10}^{-34}}{0.060\times 1}=1.1\times {10}^{-32}m\end{array}$

(c)
Hint: \(\lambda=\frac{h}{mv}\)

Step 1: Find the wavelength of the dust particle.
Mass of the dust particle,$\mathrm{m} = 1 \mathrm{x} {10}^{-9}$ kg
Speed of the dust particle, v = 2.2 m/s

De Broglie wavelength of the dust particle is given by the relation:

$\begin{array}{l}\lambda =\frac{h}{mv}\\ =\frac{6.6\times {10}^{-34}}{2.2\times 1\times {10}^{-9}}=3.0\times {10}^{-35}m\end{array}$