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)
Given: the mass of the bullet is 0.040 kg , the speed of the bullet is 1.0 km/s .
de Broglie wavelength of the bullet is given as,
λ = h m υ
Where, the mass of bullet is m , the de Broglie wavelength of bullet is λ , the speed of the bullet is υ , Planck’s constant is h .
Since, 1 km = 1000 m .
By substituting the given values in the above formula, we get
λ = 6.63 × 10 − 34 0.040 × 1000 = 1.65 × 10 − 35 m
Thus, de Broglie wavelength of bullet is 1.65 × 10 − 35 m .
(b)
Given: the mass of the ball is 0.060 kg , the speed of the ball is 1.0 m/s .
de Broglie wavelength of the bullet is given as,
λ = h m υ
By substituting the given values in the above formula, we get
λ = 6.6 × 10 − 34 0.060 × 1 = 1.1 × 10 − 32 m
Thus, de Broglie wavelength of ball is 1.1 × 10 − 32 m .
c)
Given: the mass of the dust particle is 1 × 10 − 9 kg , the speed of the dust particle is 2.2 m/s .
de Broglie wavelength of the bullet is given as,
λ = h m υ
By substituting the given values in the above formula, we get
λ = 6.6 × 10 − 34 2.2 × 1 × 10 − 9 = 3.0 × 10 − 25 m
Thus, de Broglie wavelength of dust particle is 3.0 × 10 − 25 m .
a)
Given: the mass of the bullet is
de Broglie wavelength of the bullet is given as,
Where, the mass of bullet is
Since,
By substituting the given values in the above formula, we get
Thus, de Broglie wavelength of bullet is
(b)
Given: the mass of the ball is
de Broglie wavelength of the bullet is given as,
By substituting the given values in the above formula, we get
Thus, de Broglie wavelength of ball is
c)
Given: the mass of the dust particle is
de Broglie wavelength of the bullet is given as,
By substituting the given values in the above formula, we get
Thus, de Broglie wavelength of dust particle is
