Q. 154.3( 9 Votes )

# 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?

Answer :

Now, we know de Broglie wavelength of Particle can be given by relation

Where, 𝜆 is de Broglie wavelength of a Particle

m, mass of the body

v, velocity of the body

h, planck constant = 6.63 × 10^{-34} Js

(a)

given,

mass of bullet, m = 0.040 kg

the speed of bullet is, v = 1.0 km/s = 1000 m/s

putting the valued of m, v, h in the relation

we get the de Broglie wavelength of Bullet as

So, de Broglie wavelength of Bullet is 1.65 × 10^{-35} m

(b)

given,

mass of Ball m = 0.060 kg

the speed of Ball is, v = 1.0 m/s

putting the valued of m , v, h in the relation

we get the de Broglie wavelength of Ball as

So, de Broglie wavelength of Ball is 1.1 × 10^{-32} m

(c)

given,

mass of dust particle m = 1 × 10^{-9} kg

the speed of dust particle is

v = 2.2 m/s

putting the valued of m, v, h

we get the de Broglie wavelength of Ball as

So, de Broglie wavelength of Dust Particle is 3.0 × 10^{-25} m

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