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?

Ans (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 x 10⁻³⁴ Js

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

λ=h/mv

=( 6.6 x 10⁻³⁴)/(0.040) (1000) = 1.65 x 10 ⁻³⁵ m

Ans (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:

λ=h/mv

=( 6.6 x 10⁻³⁴)/(0.060) (1) = 1.1 x 10 ⁻³² m

Ans (c).

Mass of the dust particle, m = 1 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:

λ=h/mv

=( 6.6 x 10⁻³⁴)/(2.2) (1 x 10^-9) = 3.0 x 10 ⁻²⁵ m