Electrons moving in a beam have the same de Broglie wavelength as protons in a separate beam moving at a speed of 2.8 × 10^4 m/s . What is the speed of the electrons?
de Broglie wavelength formula:
λ = h/mv,
whereλ = wavelength,h = Planck's Constant = 6.626 x 10-34 Js,m = mass of object,v = object's velocity,
Mass of proton mp = 1.6726219 × 10-27 kg,Velocity of proton vp = 2.8 × 104 ms-1 ,Mass of electron me = 9.11 × 10-31 kg,
de Broglie wavelength of proton λp= h/mpvp = (6.626x10-34)/[(1.6726219 × 10-27)(2.8 × 104)] = 1.4170 x 10-11 m,de Broglie wavelength of electron λe= h/meve = λp= 1.4170 x 10-11 m,
Rearranging for ve, we get,
ve= h/λeme, ve = (6.626x10-34)/[(1.4170 x 10-11)(9.11 × 10-31)],ve = 5.1328 x 107 ms-1,ve = 5.1 x 107 ms-1 (correct to 2 significant figures)
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