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Question 15

# 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?

(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: λ = h/mv

= 6.6 x 10-34 / 0.040 x 1000 = 1.65 x 10-35 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: λ = h/mv

= 6.6 x 10-34 / 0.060 x 1 = 1.1 x 10-32 m

(c) Mass of the dust particle, m = 1 × 109 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 x 1 x 10-9 = 3.0 x 10-25 m

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