Calculate the wavelength of
(a) a 140 g ball moving at 40 m/s
(b) a proton moving at the same speed
(c) an electron moving at the same speed.

(Answer: (a) 1.18 ｘ 10⁻³⁴ m  (b) 9.92 nm (c) 1.82 ｘ 10⁻⁵ m)



Given Data:

The velocity of the ball = Velocity of the proton = Velocity of the electron = v = 40 m s⁻¹

Mass of the ball = mb = 140 g = 0.14 kg

Mass of proton = mp = 1.67 ｘ 10⁻²⁷ kg

Mass of electron = me = 9.11 ｘ 10⁻³¹ kg


∴ Plank's Constant = h =  6.626 ｘ 10⁻³⁴ m² kg s⁻¹

To Find:

(a) Wavelength of ball = λb =  ? 

(b) Wavelength of ball = λp =  ? 

(c) Wavelength of ball = λn =  ? 



Solution:


We know that momentum P is given by

P = hλ


or


λ = hP


but P = mv , So


λ = hmv ------------(1)


(a) Wavelength of ball = λb =  ? 

Using equation (1)

λb = hmbv

by putting values

λb = 6.626ｘ10⁻³⁴m²kgs⁻¹0.14kgｘ40ms⁻¹

λb = 6.626ｘ10⁻³⁴m²kgs⁻¹5.6kgms⁻¹

λb = 1.193 ｘ 10⁻³⁴ m --------------Ans. 1



(b) Wavelength of Proton = λp =  ? 

Using equation (1)

λp = hmpv

by putting values

λp = 6.626ｘ10⁻³⁴m²kgs⁻¹1.67ｘ10⁻²⁷kgｘ40ms⁻¹

λp = 6.626ｘ10⁻³⁴m²kgs⁻¹66.8ｘ10⁻²⁷kgms⁻¹

λp = 0.0992 ｘ 10⁻⁷ m

or

λp = 9.92 ｘ 10⁻⁹ m 

or

λp = 9.92 nm --------------Ans. 2


(c) Wavelength of Electron = λe =  ? 

Using equation (1)

λe = hmev

by putting values

λe = 6.626ｘ10⁻³⁴m²kgs⁻¹9.11ｘ10⁻³¹kgｘ40ms⁻¹

λe = 6.626ｘ10⁻³⁴m²kgs⁻¹364.4ｘ10⁻³¹kgms⁻¹

λe = 0.01818 ｘ 10⁻³ m

or

λe = 1.818 ｘ 10⁻⁵ m --------------Ans. 3




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