# What is the de Broglie wavelength of

Question:

What is the de Broglie wavelength of

(a) a bullet of mass 0.040 kg travelling at the speed of 1.0 km/s,

(b) a ball of mass 0.060 kg moving at a speed of 1.0 m/s, and

(c) a dust particle of mass 1.0 × 10−9 kg drifting with a speed of 2.2 m/s?

Solution:

(a)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 × 10−34 Js

De Broglie wavelength of the bullet is given by the relation:

$\lambda=\frac{h}{m v}$

$=\frac{6.6 \times 10^{-34}}{0.040 \times 1000}=1.65 \times 10^{-35} \mathrm{~m}$

(b) 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:

$\lambda=\frac{h}{m v}$

$=\frac{6.6 \times 10^{-34}}{0.060 \times 1}=1.1 \times 10^{-32} \mathrm{~m}$

(c)Mass of the dust particle, m = 1 × 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:

$\lambda=\frac{h}{m v}$

$=\frac{6.6 \times 10^{-34}}{2.2 \times 1 \times 10^{-9}}=3.0 \times 10^{-25} \mathrm{~m}$