An electron has a de Broglie wavelength ? = 4.3 10-10 m. (a) What is its momentum? kg·m/s (b) What is its speed? m/s (c) What voltage was needed to accelerate it to this speed?
de Broglie wavelength ? = 4.3 x 10^-10 m.
mass of the electron m = 9.0 x 10^-31 kg
Plank's constant, h = 6.626 x 10^-34 J.s.
(a) Momentum P = h / ?= (6.626 x 10^-34) / (4.3 x 10^-10) = 1.541 x 10^-24 kg*m/s
(b) Momentum P =m*v
=> v = P / m = (1.541 x 10^-24) / (9.0 x 10^-31) = 0.1712 x 10^7 = 1.712 x 10^6 m/s
(c) E = qv
=> v=E/q
again -
E=P^2/2m
v = P^2/(2m*q)
put the values-
v = (1.541 x 10^-24 )^2 / (2*9.0 x 10^-31 x 1.6 x 10^-19) = 0.0825 x 10^2 = 8.25 Volt.
So the requisite voltage = 8.25 V.
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